Module 4 Time Value of Money Concepts and Calculations Flashcards
An investor wants to have $150,000 available at the end of 15 years. He plans to make equal year-end payments in an investment expected to yield a 10% annual rate of return. What is the approximate annual amount of each of these payments?
A)
$4,721
B)
$4,292
C)
$7,388
D)
$10,000
The answer is $4,721.
END Mode
1, DOWNSHIFT, P/YR
C ALL
150,000, FV
15, DOWNSHIFT, N (15 periods on display)
10, I/YR;
Solve for PMT = –4,721.0665, or $4,721 rounded.
LO 4.1.6
Abdullah needs an income stream equivalent to $50,000 in today’s dollars at the beginning of each year for the next 12 years to maintain his standard of living. He assumes inflation will average 4.5% over the long term and he can earn a 9% compound annual after-tax rate of return on investments. What lump sum does Abdullah need to invest today to fund his income need?
A)
$480,878.04
B)
$455,929.00
C)
$476,445.85
D)
$461,025.81
The answer is $480,878.04.
BEG Mode
1, DOWNSHIFT, P/YR
C ALL
50,000, PMT
[(1.09 ÷ 1.045) − 1] × 100 = 4.3062, I/YR
12, DOWNSHIFT, N (12 periods on display)
Solve for PV = -480,878.0383, or $480,878.04 rounded.
LO 4.2.4
A client wants to save $125,000 to achieve a future goal. He has $26,000 to invest and can invest another $2,500 at the end of each quarter toward his goal. If the investment vehicle selected earns 10% annually, how many years will it take to achieve his goal?
A)
5.87
B)
5.46
C)
6.06
D)
4.34
The answer is 5.87.
END Mode
4, DOWNSHIFT, P/YR
C ALL
10, I/YR
26,000, +/‒, PV
2,500, +/‒, PMT
125,000, FV
Solve for N = 23.4815 ÷ 4 quarters per year = 5.8704, or 5.87 years rounded
LO 4.2.4
Roberto purchased 80 acres of land four years ago to develop a winery. His purchase price was $1,425 an acre. At the end of each of the past four years, he incurred the following expenses or received the following cash payments to develop the vineyard:
Year 1—purchase of plants: $12,450
Year 2—
income from wine tours: $1,295
vineyard management for year: $3,270
Year 3—vineyard management for year: $3,860
Year 4—vineyard management and equipment: $6,300
At the end of the fourth year, Roberto had the property appraised and found that its value had increased to $2,000 per acre. What has been the internal rate of return for this investment over the four-year period?
A)
3.54%
B)
4.03%
C)
3.15%
D)
6.30%
The answer is 4.032%.
END Mode
1, DOWNSHIFT, P/YR
C ALL
CF0: 114,000, +/-
CF1: 12,450, +/-
CF2: 1,975, +/-
CF3: 3,860, +/-
CF4: 153,700
DOWNSHIFT, IRR/YR = 4.032, or 4.03% rounded.
LO 4.3.1
Ellen is considering investing in a piece of equipment for her business. The purchase price is $100,000, and she expects to be able to sell the equipment for $40,000 at the end of five years. During the five-year period, she expects the equipment to increase her annual cash flows by $25,000, $30,000, $20,000, $15,000, and $10,000. What is the internal rate of return (IRR) of this investment?
A)
15.79%
B)
−11.39%
C)
11.39%
D)
8.78%
The answer is 11.39%.
END Mode
1, DOWNSHIFT, P/YR
C ALL
100,000, +/-, CFj (for year 0)
25,000, CFj (year 1)
30,000, CFj (year 2)
20,000, CFj (year 3)
15,000, CFj (year 4)
50,000, CFj (year 5; final annual cash flow of $10,000 plus the anticipated sale price of $40,000); DOWNSHIFT, IRR/YR = 11.3874, or 11.39%..
LO 4.3.1
Today, Bob purchased an investment-grade gold coin for $50,000. He expects the coin to increase in value at a rate of 12% compounded annually for the next five years. How much will the coin be worth at the end of the fifth year if he achieves his expected return?
A)
$89,542.38
B)
$66,911.28
C)
$89,792.82
D)
$88,117.08
The answer is $88,117.08.
END Mode
1, DOWNSHIFT, P/YR
C ALL
50,000, +/‒, PV
12, I/YR
5, DOWNSHIFT, N (5 periods on display)
Solve for FV = 88,117.0842, or $88,117.08 rounded.
LO 4.1.2
Nick purchased 100 shares of a limited partnership for $150 per share. At the end of two years, he sold all the shares for $250 per share. At the end of each year, the investment paid a dividend of $1.50 per share. What was the investment’s internal rate of return (IRR) over the two-year period?
A)
21.82%
B)
19.07%
C)
29.99%
D)
12.45%
The answer is 29.99%.
END Mode
1, DOWNSHIFT, P/YR
C ALL
15,000, +/‒, CFj (year 0)
150, CFj (year 1)
25,150, CFj (year 2); DOWNSHIFT, IRR/YR = 29.9871, or 29.99%.
LO 4.3.1
Phan expects to receive $5,000 at the end of each of the next four years. His opportunity cost is 14% compounded annually. What is this sum worth to Phan today?
A)
$17,165.41
B)
$19,568.56
C)
$14,568.56
D)
$16,608.16
The answer is $14,568.56.
END Mode
1, DOWNSHIFT, P/YR
C ALL
5,000, PMT
14, I/YR
4, DOWNSHIFT, N (4 periods on display)
Solve for PV = -14,568.5615, or $14,568.56 rounded.
LO 4.1.3
Calculate the number of years it will take $2,500 to grow to $25,000, assuming an annual rate of return of 7% (rounded to two decimal places).
A)
34.03
B)
33.65
C)
34.43
D)
35.00
The answer is 34.03.
2,500, +/‒, PV
7, I/YR
25,000, FV
Solve for N = 34.0324 (34.03, rounded)
LO 4.1.5
Fritz has asked his financial adviser how much he would accumulate if he were to start adding $5,000 at the end of each year for the next 20 years to his investment account, which is currently worth $22,450. He anticipates earning an average annual return of 6.5% on his investments. What would Fritz’s investment account be worth in 20 years, assuming he earns this annual rate of return?
A)
$285,851
B)
$308,622
C)
$273,232
D)
$296,773
The answer is $273,232.
END Mode
1, DOWNSHIFT, P/YR
C ALL
22,450, +/-, PV
5,000, +/-, PMT
20, DOWNSHIFT, N (20 periods on display)
6.5, I/YR
Solve for FV = 273,232.3750, or $273,232 rounded.
LO 4.2.1
Pete would like to purchase a boat in 10 years for $40,000. Approximately how much should he invest at the beginning of each quarter to have enough money to purchase the boat if he can earn 6% annual interest, compounded quarterly, on his investment?
A)
$726
B)
$530
C)
$606
D)
$737
The answer is $726.
BEG Mode
4, DOWNSHIFT, P/YR
C ALL
40,000, FV
6, I/YR
10, DOWNSHIFT, N (40 periods on display)
Solve for PMT = −726.1912, or $726 rounded
LO 4.1.6
Juanita deposits $1,000 into an account earning an annual interest rate of 8% compounded monthly. Assuming she makes no withdrawals or additions to this account, approximately how many years will it take for Juanita to double her money?
A)
10.00
B)
8.00
C)
8.69
D)
8.25
The answer is 8.69.
END Mode
12, DOWNSHIFT, P/YR
C ALL
1,000, +/−, PV
2,000, FV
8, I/YR
Solve for N = 104.3183 ÷ 12 months = 8.6932, or 8.69 years rounded.
LO 4.1.5
Andrea wants to invest $2,000 annually at the end of each year into her Roth IRA. How much will she have in her account after 15 years if she can achieve a 9% annual earnings rate?
A)
$33,572
B)
$37,671
C)
$63,069
D)
$58,722
The answer is $58,722.
END Mode
1, DOWNSHIFT, P/YR
C ALL
- PV
2,000, +/−, PMT
9, I/YR
15, DOWNSHIFT, N
Solve for FV = 58,721.8324, or $58,722 rounded.
LO 4.1.2
Calculate the following inflation-adjusted return based on the following rates: 4.5% rate of return, 2% inflation rate.
A)
2.50%
B)
2.45%
C)
2.75%
D)
2.25%
The answer is 2.45%.
[(1.045 ÷ 1.02) ‒ 1] × 100 = 2.4510 (2.45, rounded)
Note: Alternate calculation for this problem would be 1.02, INPUT 1.045, DOWNSHIFT, % CHG
Solve for I/YR = 2.45%
LO 4.2.2
Calculate the following inflation-adjusted return based on the following rates: 7% rate of return, 2.5% inflation rate.
A)
1.04%
B)
2.80%
C)
4.39%
D)
0.36%
The answer is 4.39%. [(1.07 ÷ 1.025) ‒ 1] × 100 = 4.3902 (4.39, rounded)
Note: Alternate calculation for this problem would be 1.025, INPUT
1.07, DOWNSHIFT, % CHG
Solve for I/YR = 4.39%
LO 4.2.2
Liang secures a $350,000 mortgage with a 15-year repayment term and an annual interest rate of 4%. What is the monthly payment on Liang’s mortgage?
A)
$2,580.31
B)
$2,588.91
C)
$2,357.45
D)
$2,625.01
The answer is $2,588.91.
END Mode
12, DOWNSHIFT, P/YR
C ALL
350,000, PV;
15, DOWNSHIFT, N (180 periods on display)
4, I/YR
Solve for PMT = –2,588.9077, or $2,588.91 rounded.
LO 4.2.1
As Jamie Manor approaches retirement, she wants to establish a fund that will provide her with $6,000 per year after retirement to supplement her other income. Assuming that she can earn 5.5% and that she takes interest only from the fund, how much must Jamie have at retirement to provide this income?
A)
$140,099
B)
$109,091
C)
$71,702
D)
$103,600
The answer is $109,091. This is simply a calculation for capitalization of a number. On any calculator, divide the desired income, $6,000, by the decimal equivalent of the expected interest rate, .055. There is nothing in the question indicating a desire to maintain purchasing power. Additionally, when interest only is being taken from the fund, the principal is being retained so that the income will be provided indefinitely.
LO 4.1.1
Catherine expects to receive $95,000 in six years as part of a final settlement of a testamentary trust. How much would this be worth in today’s dollars assuming an 8% after-tax interest rate, compounded annually?
A)
$59,866
B)
$59,604
C)
$58,878
D)
$58,855
The answer is $59,866.
END Mode
1, DOWNSHIFT, P/YR
C ALL
95,000, FV
8, I/YR
6, DOWNSHIFT, N (6 periods on display)
Solve for PV = −59,866.1146, or $59,866 rounded.
LO 4.1.3
What is the inflation adjusted return for a portfolio that has earned 7.8% while the inflation rate has been 1.9%?
A)
5.79%
B)
6.01%
C)
5.90%
D)
5.84%
The answer is 5.79%.
1.019, INPUT
1.078, DOWNSHIFT, % CHG = 5.79%
For a reality check you should make sure the inflation adjusted rate is lower than the simple difference between the rate of return and the inflation rate. The difference between the 7.8% rate of return and 1.9% inflation rate in this example is 5.9%, and the inflation adjusted return of 5.79%, which is less.
LO 4.2.2
Joellen wants to save $500,000 (in today’s dollars) for her retirement, which is 25 years away, by depositing money in an investment at the end of every year using the serial payment method. She assumes she can earn 9% on her investment and that inflation will average 4% over the 25-year savings period. How much will Joellen need to deposit at the end of the second year to meet her goal?
A)
$11,634.87
B)
$10,757.09
C)
$10,326.81
D)
$11,187.37
The answer is $11,634.87.
END Mode
1, DOWNSHIFT, P/YR
C ALL
500,000, FV
[(1.09 ÷ 1.04) − 1 × 100] = 4.8077, I/YR
25, DOWNSHIFT, N (25 periods on display)
Solve for PMT = –10,757.0884
A payment of –10,757.0884 × 1.04 inflation rate = 11,187.3720 (end of 1st year, change sign)
A payment of 11,187.3720 × 1.04 = 11,634.8669, or $11,634.87 (rounded; end of 2nd year).
LO 4.2.3
Bernie and Betty purchased their home eight years ago for $239,500. They made a 20% down payment, and financed the balance using a 30-year mortgage with a 5.15% interest rate. Taxes and insurance increase the payment by $300 per month. What is their outstanding principal balance?
A)
$206,338
B)
$129,524
C)
$164,365
D)
$165,071
The answer is $165,071.
END Mode
12, DOWNSHIFT, P/YR
C ALL
191,600, PV ($239,500, the purchase price, less $47,900, the 20% down payment.)
30, DOWNSHIFT, N (360 periods on display)
5.15, I/YR
Solve for PMT = $1,046.1862
1, INPUT, 96, DOWNSHIFT, AMORT (1 – 96 on display)
Pressing the = key toggles you through amortization totals for months 1 – 96:
Enter = and the principal paid thus far in eight years will display: -26,529.4379
Enter = again and interest paid to date displays:-73,904.4373
Enter = one final time and the remaining principal balance will be displayed: $165,070.5621, rounded to $165,071
LO 4.2.1
Kieran is interested in investing $50,000 in the stock of a new company. The stock will pay no dividends, but Kieran anticipates he will be able to sell the investment for $75,000 in two years. If his required rate of return is 9%, what is the net present value (NPV) of this investment?
A)
$13,126
B)
$113,126
C)
−$13,126
D)
$18,807
The answer is $13,126.
END Mode
1, DOWNSHIFT, P/YR
C ALL
50,000, +/–, CFj (for year 0)
0, CFj (for year 1)
75,000, CFj (for year 2)
9, I/YR; DOWNSHIFT, NPV = 13,125.9995, or $13,126 rounded.
LO 4.3.2
Sam purchased a certificate of deposit yielding 3% annually for $6,000. Today, it matured for $12,004.25. Approximately how many years did Sam own the certificate of deposit (rounded to the nearest 0.00)?
A)
25.55
B)
23.40
C)
24.03
D)
23.46
The answer is 23.46.
END Mode
1, DOWNSHIFT, P/YR
C ALL
3, I/YR
-6,000, PV
12,004.25, FV
Solve for N = 23.4618, or 23.46 rounded.
LO 4.1.5
What is the present value of an investment that would provide the following inflows, assuming that the client’s required compound rate of return is 9%?
End of year Amount
1 $15,000
2 $20,000
3 $22,000
4 $25,000
A)
$65,646.99
B)
$65,433.45
C)
$65,543.90
D)
$65,293.73
The answer is $65,293.73.
END Mode
1, DOWNSHIFT, P/YR
C ALL
0, CFj
15,000, CFj
20,000, CFj
22,000, CFj
25,000, CFj
9, I/YR
DOWNSHIFT, NPV = $65,293.73.
LO 4.3.2
Sarah wishes to start saving for a lump-sum amount of $100,000 (in today’s dollars) that is needed in four years. She assumes an inflation rate of 3% and an investment rate of return of 7.5%. Calculate Sarah’s deposit (PMT) in the second year using the serial payment method if she were to deposit the needed savings at the end of each of the four years.
A)
$24,846.28
B)
$23,420.00
C)
$25,591.67
D)
$24,122.60
The required deposit at the end of the second year using the serial payment approach is $24,846.28.
END Mode
1, DOWNSHIFT, P/YR
C ALL
100,000 FV
[(1.075 ÷ 1.03) – 1] × 100 = 4.3689, I/YR
4, DOWNSHIFT, N (4 periods on display)
Solve for PMT = -23,420.0027, or $23,420.00 (change sign)
End of year 1: $23,420.00 × 1.03 = $24,122.60
End of year 2: $24,122.60 × 1.03 = $24,846.28
LO 4.2.3
The required deposit at the end of the second year using the serial payment approach is $24,846.28.
END Mode
1, DOWNSHIFT, P/YR
C ALL
100,000 FV
[(1.075 ÷ 1.03) – 1] × 100 = 4.3689, I/YR
4, DOWNSHIFT, N (4 periods on display)
Solve for PMT = -23,420.0027, or $23,420.00 (change sign)
End of year 1: $23,420.00 × 1.03 = $24,122.60
End of year 2: $24,122.60 × 1.03 = $24,846.28
LO 4.2.3
The $10,000 sum will take approximately 12 years to grow to $25,000.
END Mode
1, DOWNSHIFT, P/YR
C ALL
10,000, +/−, PV
25,000, FV
8, I/YR
Solve for N = 11.9059 or, 12 years (rounded).
LO 4.1.5
Eugene wants to purchase a fishing camp in five years for $60,000. What periodic payment should he invest at the beginning of each quarter to attain the goal if he can earn a 10.5% annual rate of return, compounded quarterly on investments?
A)
$2,319.42
B)
$2,260.09
C)
$9,730.53
D)
$8,805.91
The answer is $2,260.09.
BEG Mode
4, DOWNSHIFT, P/YR
C ALL
60,000, FV
10.5, I/YR
5 DOWNSHIFT, N (20 periods on display)
Solve for PMT = ‒2,260.0924, or $2,260.09 rounded.
LO 4.1.6
Jonathan has become one of the beneficiaries of his uncle’s trust fund and he will receive $10,000 at the beginning of each year for the next 20 years. What is the present value of this annuity income stream, assuming one could earn a 4% annual rate of return?
A)
$154,666
B)
$135,903
C)
$129,608
D)
$141,339
The answer is $141,339.
BEG Mode
1, DOWNSHIFT, P/YR
C ALL
10,000, PMT
20, DOWNSHIFT, N
4, I/YR
Solve for PV = $141,339 rounded
LO 4.1.3
George and Chelsea want to make sure they will have enough funds available to send their son Oliver to college. Oliver is eight years old and will begin a four-year college program at age 20 after working full time for two years following high school graduation. The annual tuition today is $10,000, and it is expected to increase annually by 5%. George and Chelsea estimate that they can get a 7% after-tax return on their money.
If George or Chelsea were to die, what would be the amount of insurance needed today to provide for Oliver’s education?
A)
$30,970
B)
$30,433
C)
$31,012
D)
$30,363
The answer is $31,012. The answer is calculated by inflating the $10,000 at 5% for 12 years = $17,959. Next, enter $17,959 as the first PMT, and calculate the PVAD (BEGIN) for four years using the inflation-adjusted interest rate (1.9048) = $69,845. Finally, enter $69,845 as a FV, discounted at the after-tax return of 7% for 12 years, and solve for the PV ($31,012).
Keystrokes:
Step 1
END Mode
1, DOWNSHIFT, P/YR
C ALL
12, DOWNSHIFT, N (12 periods on display)
5, I/YR
10,000, +/-, PV
Solve for FV = 17,958.5633
Step 2
BEG Mode
1, DOWNSHIFT, P/YR
C ALL
4, DOWNSHIFT, N (4 periods on display)
1.9048, I/YR This is ([1.07 ÷ 1.05] – 1) x 100.
17,958.5633, +/-, PMT
0, FV
Solve for PV = 69,845.1886
Step 3
END Mode
1, DOWNSHIFT, P/YR
C ALL
12, N
7, I/YR
69,845.1886, FV
Solve for PV = 31,012.0990, or $31,012 rounded.
LO 4.2.3
Jake borrowed $18,000 from his father to purchase a camper. Jake repaid $25,000 to his father at the end of six years. What was the average annual compound rate of interest on Jake’s loan from his father?
A)
23.15%
B)
13.81%
C)
5.27%
D)
5.63%
The answer is 5.63%.
END Mode
1, DOWNSHIFT, P/YR
C ALL
6, DOWNSHIFT, N (6 periods on display)
18,000, PV
25,000, +/‒, FV
Solve for I/YR = 5.6277, or 5.63%.
LO 4.1.4
Zoya must make payments to Don at the end of each year for the next four years. The payments will be $6,000, $6,600, $7,250, and $8,100, respectively. How much should Zoya have in her account today to meet these payments, assuming her account earns an annual interest rate of 8.5%?
A)
$27,950
B)
$25,296
C)
$28,253
D)
$22,657
The answer is $22,657.
END Mode
1, DOWNSHIFT, P/YR
C ALL
0, CF0
6,000, CF1
6,600, CF2
7,250, CF3
8,100, CF4
8.5, I/YR
DOWNSHIFT, NPV = 22,657.1942, or $22,657 rounded.
LO 4.3.1
Clayton wishes to start saving for a lump-sum amount of $75,000 (in today’s dollars) that is needed in seven years. He assumes an inflation rate of 2% and an investment rate of return of 9%. Assume Clayton wishes to save annually using the level payment method. What is his required deposit? (Round to the nearest dollar.)
A)
$8,766
B)
$8,590
C)
$9,551
D)
$9,364
The answer is $9,364.
Step 1: Inflate the lump-sum in today’s dollars into the future need.
END Mode
1, DOWNSHIFT, P/YR
C ALL
75,000, +/−, PV
7, DOWNSHIFT, N (7 periods on display)
2, I/YR
Solve for FV = 86,151.4251
Solve for the required annual level payment using the inflated lump-sum value.
DOWNSHIFT, C ALL
FV = 86,151.4251
7, DOWNSHIFT, N (7 periods on display)
9, I/YR
Solve for PMT = –9,363.8429, or $9,364 rounded.
LO 4.1.6
Sam received a small windfall years ago of $4,000 and promptly invested it in a fund that he then forgot about. Several years later, he rediscovered that the account existed and that it was now worth $7,356, having earned an annual return of 5.4%. How many years had transpired since Sam had invested his small windfall?
A)
10½ years
B)
12½ years
C)
14½ years
D)
11½ years
The answer is 11½ years.
END Mode
1, DOWNSHIFT, P/YR
C ALL
4,000 +/-, PV
7,356, FV
5.44, I/YR
Solve for N = 11.50
LO 4.1.5
Frank wants to achieve a 7% annual rate of return, and anticipates that inflation will be 2%. What would his inflation adjusted return be?
A)
4.9%
B)
5.0%
C)
4.7%
D)
4.8%
The answer is 4.9%.
1.02, INPUT
1.07, DOWNSHIFT, % CHG = 4.90%
For a reality check you should make sure the inflation adjusted rate is lower than the simple difference between the rate of return and the inflation rate. The difference between the 7% rate of return and 2% inflation rate in this example is 5%, and the inflation adjusted return of 4.90%, which is less.
LO 4.2.2
Jonathan is considering the purchase of some rental property. The owner is asking $1,125,000, and the apartment units are expected to generate cash flows of $70,000, $75,000, $80,000, and $95,000 over the next four years. The property is expected to be worth $1,200,000 at the end of four years. What is the maximum amount that Jonathan should pay for the property (its intrinsic value) if her required rate of return is 9%?
A)
$1,117,884
B)
$1,106,531
C)
$1,052,667
D)
$1,125,000
The answer is $1,106,531.
END Mode
1, DOWNSHIFT, P/YR
C ALL
0, CFj
70,000, CFj
75,000, CFj
80,000, CFj
1,295,000, CFj ($95,000 + $1,200,000)
9, I/YR
DOWNSHIFT, NPV = 1,106,531.51, or 1,106,532 rounded.
LO 4.3.2
What would the inflation-adjusted interest rate be with a 7% rate of return and a 3% inflation rate (rounded to 2 decimal places)?
A)
0.96%
B)
1.04%
C)
2.33%
D)
3.88%
The answer is 3.88%. [(1.07 ÷ 1.03) ‒ 1] × 100 = 3.8835 (3.88, rounded)
Note: Alternate calculation for this problem would be 1.03, INPUT
1.07, DOWNSHIFT, % CHG
Solve for I/YR = 3.88%
LO 4.2.2
A client wishes to accumulate $90,000 for a future goal in seven years. She can deposit $32,000 today in an account earning 11% annual interest and plans to make an additional payment into the account at the end of each year. What periodic payment will be required at the end of each year to meet her goal?
A)
$1,434.70
B)
$2,408.49
C)
$1,340.84
D)
$2,169.81
The periodic payment required each year is $2,408.49.
END Mode
1, DOWNSHIFT, P/YR
C ALL
11, I/YR
32,000, +/‒, PV
90,000, FV
7, DOWNSHIFT, N (7 periods on display)
Solve for PMT = $2,408.49.
LO 4.2.4
Six years ago, a client invested $5,000 in a mutual fund. He made additional investments of $300 at the end of each year. Yesterday, the client redeemed all fund shares and received $8,500. What was the rate of return on this investment?
A)
4.24%
B)
4.44%
C)
4.06%
D)
4.25%
The rate of return has been 4.44% annually.
END Mode
1, DOWNSHIFT, P/YR
C ALL
5,000, +/‒, PV
8,500, FV
300, +/‒, PMT
6, DOWNSHIFT, N (6 periods on display)
Solve for I/YR = 4.4378, or 4.44%.
LO 4.2.4
Gregos received an inheritance of $200,000. He wants to withdraw equal periodic payments at the beginning of each month for the next five years. He expects to earn a 12% annual rate of return, compounded monthly on his investments. How much can Gregos receive each month?
A)
$49,537.45
B)
$4,448.89
C)
$55,481.95
D)
$4,404.84
The answer is $4,404.84.
BEG Mode
12, DOWNSHIFT, P/YR
C ALL
200,000, PV
12, I/YR
5, DOWNSHIFT, N (60 periods on display)
Solve for PMT = -4,404.8411, or $4,404.84 rounded.
LO 4.1.6
Luna is considering investing in a piece of equipment for her business. The purchase price of the equipment is $100,000, and she expects to be able to sell it for $40,000 at the end of five years. During the five-year period, Luna expects the equipment to increase her annual cash flows by $25,000, $30,000, $20,000, $15,000, and $10,000. If her opportunity cost is 8%, what is the net present value (NPV) of this investment?
A)
$209,799.56
B)
$9,799.57
C)
$109,799.56
D)
−$17,423.76
The answer is $9,799.57.
END Mode
1, DOWNSHIFT, P/YR
C ALL
100,000, +/‒, CFj (year 0)
25,000, CFj (year 1)
30,000 CFj (year 2)
20,000, CFj (year 3)
15,000, CFj (year 4)
50,000, CFj (year 5; final annual cash flow of $10,000 plus the anticipated sales price of $40,000); 8, I/YR, DOWNSHIFT, NPV = 9,799.5652, or $9,799.57 rounded.
LO 4.3.2
Yvonne is an advisor who uses a projected 8.4% rate of return for aggressive portfolios while also factoring in a 2.5% inflation rate. What inflation-adjusted rate of return is Yvonne using?
A)
5.70% return
B)
5.80% return
C)
5.73% return
D)
5.76% return
The answer is 5.76% return.
1.025, INPUT
1.084, DOWNSHIFT, % CHG = 5.76%
LO 4.2.2
When Graciela was born, her grandparents deposited $30,000 in an account in which interest was compounded quarterly. Twenty-one years later, the account holds $154,025. What was the annual rate of return on this investment? (Round your answer to the nearest tenth of a percent.)
A)
7.9%
B)
8.1%
C)
9.1%
D)
19.5%
The answer is 7.9%.
END Mode
4, DOWNSHIFT, P/YR
C ALL
30000, +/–, PV
21, DOWNSHIFT, N (84 periods on display)
154025, FV
SOLVE for I/YR = 7.9%
LO 4.1.4
Grace would like to purchase her uncle’s business in 10 years for $135,000. Her mother will give her $10,000 toward the purchase at that time. Grace wants to save monthly for the remaining balance. What is the approximate monthly payment at the beginning of each month needed to accumulate the $135,000, including her mother’s gift, at an assumed interest rate of 8%?
A)
$665.79
B)
$678.74
C)
$683.26
D)
$733.03
The answer is $678.74.
BEG Mode
12, DOWNSHIFT, P/YR
C ALL
125,000, FV This is the goal of $135,000 less the $10,000 gift from Grace’s mother.
8, I/YR
10, DOWNSHIFT, N (120 periods on display)
Solve for PMT = −678.7367, or $678.74 rounded.
LO 4.1.6
What would the inflation-adjusted interest rate be with a 5.5% rate of return and a 3% inflation rate (rounded to two decimal places)?
A)
2.33%
B)
1.04%
C)
2.43%
D)
0.96%
The answer is 2.43%.
[(1.055 ÷ 1.03) ‒ 1] × 100 = 2.4272 (2.43, rounded)
Note: Alternate calculation for this problem would be 1.03, INPUT, 1.055, DOWNSHIFT, % CHG
Solve for I/YR = 2.43%
LO 4.2.2
Yuri recently purchased a resort home as an investment for $500,000 in cash. She assumes she will be able to sell the home in 10 years for $850,000. If her expectations are correct, what average annual interest rate will have been earned on the investment?
A)
5.4%
B)
5.2%
C)
58.2%
D)
58.8%
The answer is 5.4%.
END Mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
500,000, +/-, PV
850,000, FV
10, DOWNSHIFT, N
Solve for I/YR = 5.4496, or 5.4% rounded
LO 4.1.4
Tisha secures a $250,000, 15-year mortgage with an annual interest rate of 5%. What will be the unpaid principal balance on Tisha’s mortgage at the end of 10 years?
A)
$104,761.78
B)
$91,999.87
C)
$145,238.22
D)
$124,875.99
The answer is $104,761.78. The keystrokes are as follows:
END Mode
12, DOWNSHIFT, P/YR
C ALL
250,000 PV
15, DOWNSHIFT, N (180 periods on display)
5, I/YR
Solve for PMT = –1,976.9841
1, INPUT, 120, DOWNSHIFT, AMORT (1–120 on display)
Pressing the = key toggles you through amortization totals for months 1–120)
Enter = and –145,238.2228 is displayed (total principal paid through 120 months)
Enter = again and –91,999.8692 is displayed (total interest paid through 120 months)
Enter = one final time and 104,761.7772 is displayed (remaining principal balance through 120 months of payments).
104,761.7772, rounded to $104,761.78 is the unpaid principal balance on Tisha’s mortgage at the end of 10 years.
LO 4.2.1
The Smiths are saving for their son Dimitri’s education and want to use a realistic inflation-adjusted rate of return for any projections. Which inflation-adjusted return would they use if they anticipate earning 6.5% on their investments and the rate of inflation is 1.7%?
A)
4.67% return
B)
4.76% return
C)
4.81% return
D)
4.72% return
The answer is 4.72% return.
1.017, INPUT
1.065, DOWNSHIFT, % CHG = 4.72%
LO 4.2.2
Julia wants to withdraw $4,000 at the beginning of each year for the next seven years from her investment account. She expects to earn a 10.5% rate of return compounded annually on her investment. What lump sum should Julia deposit today?
A)
$20,627.25
B)
$19,157.21
C)
$18,667.20
D)
$21,168.72
The answer is $21,168.72.
BEG Mode
1, DOWNSHIFT, P/YR
C ALL
4,000, PMT
10.5, I/YR
7, DOWNSHIFT, N
Solve for PV = -21,168.7176, or $21,168.72 rounded.
LO 4.1.3
Salina wants to receive payments of $5,000 at the beginning of each month during her retirement. Megan estimates she will need to receive this monthly payment for 30 years. If a 6% annual return is earned on investments, compounded monthly, what amount must Salina have at the time of her retirement to fund her needs?
A)
$838,128
B)
$5,047,688
C)
$5,022,575
D)
$833,958
The answer is $838,128.
BEG Mode
12, DOWNSHIFT, P/YR
C ALL
30, DOWNSHIFT, N (360 periods on display)
6, I/YR
5,000, PMT
Solve for PV = 838.128.
Note that there is nothing in this question that indicates a desire to maintain purchasing power, so inflation is not a factor.
LO 4.1.3
Joan Greene invested $50,000 in an account earning 6% annual interest, compounded quarterly. How much will the account be worth if the sum is left in the account for 15 years?
A)
$62,512
B)
$122,161
C)
$120,465
D)
$119,828
The answer is $122,161.
END Mode
4, DOWNSHIFT, P/YR
DOWNSHIFT C ALL
$50,000, +/-, PV
6, I/YR
15, DOWNSHIFT, N
Solve for FV = $122,161.
LO 4.1.2
Bernie Swenson wants to pay the college costs for his daughter Becky, who will be attending State College. Her annual costs are estimated to be $42,000 today. Becky is three years old and will start college in 15 years. Bernie wants to anticipate an increase in cost of approximately 6% annually. How much will Bernie need to provide for her first year of college?
A)
$133,231
B)
$100,655
C)
$50,023
D)
$42,000
The answer is $100,655.
END Mode
1, DOWNSHIFT, P/YR
C ALL
15, DOWNSHIFT, N
42,000, PV
0, PMT
Solve for FV = $100,655
LO 4.1.2
Joe purchased 100 shares of an aggressive growth mutual fund at $90 per share seven years ago. Today he sold all 100 shares for $45,000. What was his average annual compound rate of return on this investment before tax?
A)
21.73%
B)
19.58%
C)
17.46%
D)
25.85%
The answer is 25.85%.
END Mode
1, DOWNSHIFT, P/YR
C ALL
9,000, +/‒, PV This is 100 shares x $90.
45,000, FV
7, DOWNSHIFT, N (7 periods on display)
Solve for I/YR = 25.8499, or 25.85% rounded.
LO 4.1.4
Elayne and Les assume that college costs will increase at the rate of 3% annually from now through the time their son, Adam, completes college. While Adam is enrolled in college, they can achieve an after-tax rate of return of 9.5% annually on funds earmarked for this goal. Calculate the inflation-adjusted return that the couple expects while Adam is in college.
A)
6.31%
B)
1.89%
C)
1.06%
D)
6.50%
The answer is 6.31%.1.03, INPUT
1.095, DOWNSHIFT, % CHG
Solve for I/YR = 6.31%
Note: alternate calculation for this problem:
[(1.095 ÷ 1.03) ‒ 1] × 100 = 6.3107, or 6.31% rounded.
LO 4.2.2
John borrowed $800 from his father to purchase a mountain bike. John paid $1,200 back to his father at the end of five years. What was the average annual compound rate of interest on John’s loan from his father?
A)
8.45%
B)
7.79%
C)
5.20%
D)
11.56%
The answer is 8.45%.
END Mode
1, DOWNSHIFT, P/YR
C ALL
800, PV
1,200, +/‒, FV
5, DOWNSHIFT, N (5 periods on display)
Solve for I/YR = 8.4472 or 8.45% rounded.
LO 4.1.4
Sachi wants to start her own business in four years. She must accumulate $175,000 in today’s dollars to sufficiently finance her business in four years. She assumes that inflation will average 5% and that she can earn a 9% compound annual after-tax return on investments. What serial payment should Sachi invest at the end of the first year to attain her goal?
A)
$41,327.87
B)
$43,394.26
C)
$48,438.44
D)
$38,320.82
The answer is $43,394.26.
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
175,000, FV
4, DOWNSHIFT, xP/YR (4 appears on display)
(1.09 ÷ 1.05) – 1 × 100 = 3.8095, I/YR or I/Y
Solve for PMT = -41,327.8745 × 1.05 = $43,394.26
LO 4.2.3
Felix wants to save an additional $250,000 for his retirement in 10 years. He has accumulated $74,000 so far, and he wants to use 5% as his annual rate of return. How much would Felix need to deposit at the end of each year in order to reach his goal of accumulating a total of $250,000?
A)
$10,003
B)
$10,293
C)
$10,414
D)
$10,556
The answer is $10,293.
END Mode
1, DOWNSHIFT, P/YR
C ALL
74,000, +/-, PV
250,000, FV
10, DOWNSHIFT, N (10 periods on display)
5, I/YR
Solve for PMT= 10,292.80, or $10,293 rounded.
LO 4.2.4
Stu wants to accumulate $20,000 in 18 years. He expects to earn an average annual compound return of 8%. The market has been depressed lately. What periodic payment should he invest at the beginning of each of the next 18 years to reach his goal? (Round your answer to the nearest dollar.)
A)
$534
B)
$1,111
C)
$494
D)
$988
The answer is $494.
BEG Mode
1, DOWNSHIFT, P/YR
C ALL
20,000, FV
18, DOWNSHIFT, N (18 periods on display)
8, I/YR
Solve for PMT = -494.4833, or $494 rounded.
LO 4.1.6
Mary plans to give her granddaughter, Jessica, $5,000 at the end of each year for the next five years. Jessica plans to invest the money and assumes she can earn 6% annually on the investment. What is the approximate present value of this sum?
A)
$26,495
B)
$21,552
C)
$21,062
D)
$22,323
The answer is $21,062.
END Mode
1, DOWNSHIFT, P/YR
C ALL
5,000, +/-, PMT
6, I/YR
5, DOWNSHIFT, N (5 periods on display)
Solve for PV = 21,061.8189, or $21,062 rounded.
LO 4.1.3
Carlotto invested $12,000 in an account earning 6.5% annual interest, compounded monthly. Approximately how many years will it take for the account to be worth $100,000?
A)
35 years
B)
33 years
C)
8 years
D)
393 years
The answer is 33 years.
END Mode
12, DOWNSHIFT, P/YR
C ALL
12,000, +/-, PV]
6.5, I/YR
100,000, FV
Solve for N = 392.4924 ÷ 12 = 32.70, or 33 years rounded. (Divide your answer by 12 to determine the number of years because the result indicates the number of months).
LO 4.1.5
David, age 39, is starting his traditional IRA contributions immediately. He will invest $4,000 at the beginning of each year for the next 20 years. Assuming he earns 7.5% compounded annually on these funds, how much will David have in his IRA after the 20 years?
A)
$173,219
B)
$184,392
C)
$186,210
D)
$68,464
The answer is $186,210. This is a future value of an annuity due calculation. The keystrokes on the HP 10bII/HP 10bII+ are as follows: BEG mode; 7.5, I/YR; 20, N; 4,000, +/−, PMT; Solve for FV = 186,210.1297, or $186,210.
LO 4.1.2
Joe purchased 100 shares of an aggressive growth mutual fund at $9 per share seven years ago. Earlier today he sold all 100 shares for $4,500. What was his average annual compound rate of return on this investment before tax?
A)
17.46%
B)
21.73%
C)
25.85%
D)
19.58%
The answer is 25.85%.
END Mode
1, DOWNSHIFT, P/YR
C ALL
900, +/−, PV
4,500, FV
7, DOWNSHIFT, N (7 periods on display)
Solve for I/YR = 25.8499, or 25.85% rounded.
LO 4.1.4
Which of the following correctly states the relationship between NPV, IRR, and required return?
If NPV > 0, then IRR > required return.
If NPV = 0, then IRR = required return.
If NPV > 0, then IRR < required return.
If NPV < 0, then IRR < required return.
A)
I only
B)
I, II, and IV
C)
III and IV
D)
I, III, and IV
The answer is I, II, and IV. Only statement III is incorrect. If the NPV is a positive number, then the investor will earn a rate of return (IRR) greater than the required rate of return. Conversely, if the result of the NPV calculation is a negative number, then the investor will earn a rate of return (IRR) less than the required rate of return.
LO 4.3.1
Calculate the number of months it will take $10,000 to grow to $1,000,000 assuming an annual rate of return of 6%, compounded monthly (rounded to two decimal places).
A)
79.03
B)
923.33
C)
309.31
D)
155.80
The answer is 923.33.
END Mode
12, DOWNSHIFT, P/YR
C ALL
-10,000, PV
6, I/YR
1,000,000, FV
Solve for N = 923.3347 (923.33, rounded).
LO 4.2.3
Alexa invested a $25,000 inheritance into a balanced fund years ago, and it is now worth $102,440. If her annual rate of return has been 7.70%, compounded annually, aopproximately how many years have gone by since she initially invested in the fund?
A)
23 years
B)
19 years
C)
25 years
D)
21 years
The answer is 19 years.
END Mode
1, DOWNSHIFT, P/YR
C ALL
25,000, +/-, PV
102,440, FV
7.70, I/YR
Solve for N = 19.01, or 19 years rounded.
LO 4.1.5
Sam wants to accumulate $75,000 in seven and a half years to purchase a boat. He expects to earn an annual rate of return on invested funds of 12% compounded quarterly. How much must Sam invest today to meet his goal?
A)
$31,489
B)
$32,057
C)
$30,899
D)
$66,000
Sam must set aside $30,899 now to achieve his financial goal.
END Mode
4, DOWNSHIFT, P/YR
C ALL
75,000, FV
12, I/YR
7.5, DOWNSHIFT, N (30 periods on display)
Solve for PV = ‒30,899.0070, or $30,899 rounded.
LO 4.1.3
Darrin and Marlene Pruett are going to establish an education fund for their daughter. They want to know the best method for accumulating the most money by the time their daughter is ready for college.
Assuming the same return is earned on all of the options, which of the following will provide the greatest accumulation over a specified period of time?
A)
$100 per month invested on the first of the month, starting in 30 days
B)
$1,200 per year invested annually starting one year from now
C)
$1,200 per year invested annually starting today
D)
$100 per month invested on the first of the month, starting today
The answer is $1,200 per year invested annually starting today. This lump sum will earn interest all year. If the first payment is made in one year, a full year’s return will be lost. If payments are made monthly, only one-twelfth of the money will earn interest for the entire year.
LO 4.1.1
Finn is considering the purchase of a rental real estate property for $80,000. Because of his area’s slow real estate market, he anticipates he will not see any cash flow from this property until the end of the second year, when he estimates a cash inflow of $5,000. Finn also anticipates a cash inflow of $5,000 at the end of the third year, with subsequent cash inflows of $7,500 at the end of the fourth year and $10,000 at the end of the fifth year. At the end of the fifth year, Finn believes he can sell the property for at least $120,000. If his required rate of return is 10%, what is the net present value (NPV) of this property?
A)
$13,731
B)
$15,653
C)
$23,104
D)
$6,957
The answer is $13,731.
Be sure to input 0 as the cash flow for year 1 and to then add the final cash inflow to the sales price.
END Mode
1, DOWNSHIFT, P/YR
C ALL
80,000, +/−, CFj
0, CFj
5,000, CFj
2, DOWNSHIFT, Nj
7,500, CFj
130,000, CFj
10 I/YR; DOWNSHIFT, NPV = 13,731.1738, or $13,731 rounded.
LO 4.3.2
Tolmas wants to save $1 million (in today’s dollars) for his retirement, which is 20 years away, by depositing money in his brokerage account at the end of every year using the serial payment method. He assumes he can earn 7% on his investments and that inflation will average 3% over the 20-year savings period. How much does Tolmas need to deposit at the end of the first year to meet his goal?
A)
$33,989.70
B)
$32,970.01
C)
$35,009.39
D)
$36,368.98
The required payment at the end of the first year is $35,009.39.
END Mode
1, DOWNSHIFT, P/YR
C ALL
1,000,000, FV
[(1.07 ÷ 1.03) − 1 × 100] = 3.8835, I/YR
20, DOWNSHIFT, N (20 periods on display)
Solve for PMT = –33,989.7035
PMT of –33,989.7035 × 1.03 inflation rate = –35,009.3946, or $35,009.39 (rounded) for the deposit required at the end of the first year.
LO 4.2.3
Mike won $20 million in the state lottery. His winnings will be paid annually over 30 years in equal payments made at the end of each year. What is the present value of this sum, assuming a discount rate of a 5%?
A)
$10,392,100
B)
$4,627,549
C)
$10,248,301
D)
$10,760,716
The answer is $10,248,301.
END Mode
1, DOWNSHIFT, P/YR
C ALL
5, I/YR
30, DOWNSHIFT, N (30 periods on display)
666,666.6667, PMT (This is 20,000,000 ÷ 30 years, or the equal annual payment.)
Solve for PV = −10,248,300.6851, or $10,248,301 rounded.
LO 4.1.3
For the past 10 years, Victor has been contributing $3,000 each year into his IRA account. The IRA account is invested in an aggressive growth stock fund. He has made his contribution on the last day of each year, and his account has grown to $68,225. What annual rate of return has Victor earned?
A)
15.58%
B)
14.33%
C)
17.31%
D)
16.06%
The answer is 17.31%.
END Mode
1, DOWNSHIFT, P/YR
C ALL
3,000, +/-, PMT
68,225, FV
10, DOWNSHIFT, N
Solve for I/YR = 17.31%
LO 4.1.4
Giulia purchased an investment in a real estate limited partnership five years ago at a cost of $35,000. The partnership made the following annual distributions.
Year Amount
1 $1,725
2 $3,000
3 $1,175
4 $1,800
5 $1,440
At the time the fifth-year distribution was paid, the partnership sold the underlying property and distributed an additional $34,250 to Giulia.
What was Giulia’s average annual compound rate of return (IRR) on the partnership investment?
A)
8.034%
B)
4.017%
C)
4.882%
D)
9.440%
The answer is 4.882%.
END Mode
1, DOWNSHIFT, P/YR
C ALL
CF0: 35,000, +/-
CF1: 1,725
CF2: 3,000
CF3: 1,175
CF4: 1,800
CF5: 35,690 (34,250 + 1,440)
DOWNSHIFT, IRR/YR = 4.8817%, or 4.882.
LO 4.3.1
Clarence has been investing $1,000 at the end of each year for the past 15 years. How much has he accumulated, assuming he has earned a 10.5% rate of return compounded annually on his investment?
A)
$33,060.04
B)
$20,303.72
C)
$23,349.28
D)
$36,531.34
The answer is $33,060.04.
END Mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
1,000, +/‒, PMT
10.5, I/YR
15, DOWNSHIFT, N
Solve for FV = 33,060.0354, or $33,060.04 rounded.
LO 4.1.2
What is the present value of an investment that would provide the following inflows, assuming that the client’s required compound rate of return is 8%?
End of year Amount
1 $12,000
2 $15,000
3 $18,000
4 $22,000
A)
$54,174
B)
$54,431
C)
$54,337
D)
$54,777
The answer is $54,431.
END Mode
1, DOWNSHIFT, P/YR
C ALL
0, CFj
12,000, CFj
15,000, CFj
18,000, CFj
22,000, CFj
8, I/YR
DOWNSHIFT, NPV = $54,430.83, or $54,431 rounded.
LO 4.3.2
Zoe invested $50,000 into a speculative limited partnership that is now worth $56,800. If Zoe’s annual rate of return has been 2.13%, compounded quarterly, how long has she held the limited partnership?
A)
Seven years
B)
Five years
C)
Six years
D)
Four years
The answer is six years.
END Mode
4, DOWNSHIFT, P/YR
C ALL
50,000, +/-, PV
56,800, FV
2.13, I/YR
Solve for N = 24.0 ÷ 4 = 6.0025, or 6 years rounded.
LO 4.1.5
Robert borrowed $800 from his brother, Matt, to purchase an electric guitar. Five years later, Robert paid Matt $1,200 to settle the loan. What was the average annual compound interest rate on Matt’s loan to Robert?
A)
11.56%
B)
5.20%
C)
7.79%
D)
8.45%
The answer is 8.45%.
END Mode
1, DOWNSHIFT, P/YR
C ALL
800, PV
1,200, +/−, FV
5, DOWNSHIFT, N (5 periods on display)
Solve for I/YR = 8.4472, or 8.45% rounded.
LO 4.1.4
Cahdi wishes to accumulate a lump-sum amount of $50,000 (in today’s dollars) in five years for a down payment on a vacation villa. She assumes an inflation rate of 2.5% and a before-tax investment rate of return of 6%. If Cahdi deposits the needed savings at the end of each year for the next five years, what is her required payment in the first year using the serial payment method?
A)
$9,031.60
B)
$9,573.49
C)
$9,257.39
D)
$9,399.99
The required annual deposit under the serial payment approach is $9,573.49.
END Mode
1, DOWNSHIFT, P/YR
C ALL
50,000, FV
(1.06 ÷ 1.025) – 1] × 100 = 3.4146, I/YR
5, DOWNSHIFT, N (5 periods on display)
Solve for PMT = ‒9,399.9921; PMT of –9,399.9921 × 1.025 inflation rate = –9,573.4919, or $9,573.49 rounded.
LO 4.2.3
A client wishes to accumulate $90,000 in seven years. She can deposit $32,000 today in an account earning 11% annual interest and plans to make an additional payment into the account at the end of each year. What periodic payment will be required at the end of each year to meet her goal?
A)
$1,434.70
B)
$2,169.81
C)
$1,340.84
D)
$2,408.49
The answer is $2,408.49.
END Mode
1, DOWNSHIFT, P/YR
C ALL
90,000, FV
32,000, +/-, PV
7, DOWNSHIFT, N
11, I/YR
Solve for PMT = $2,408.49.
LO 4.1.6
Risa secures a $500,000 mortgage with a 30-year repayment term and an annual interest rate of 5.5%. What is the monthly payment on Risa’s mortgage?
A)
$2,825.99
B)
$4,085.42
C)
$2,838.95
D)
$3,757.09
The answer is $2,838.95.
END Mode
12, DOWNSHIFT, P/YR
C ALL
500,000, PV
30, N
5.5, I/YR;
Solve for PMT = –2,838.9450, or $2,838.95 rounded.
LO 4.2.1
Benito’s investment portfolio has a current balance of $100,000. Assuming his portfolio grows to $500,000 in 17 years, what is the underlying annual rate of return?
A)
11.32%
B)
9.93%
C)
10.17%
D)
9.43%
The answer is 9.93%.
END Mode
1, DOWNSHIFT, P/YR
C ALL
100,000, +/−, PV
500,000, FV
17, DOWNSHIFT, N (17 periods on display)
Solve for I/YR = 9.9299, or 9.93% rounded.
LO 4.1.4
Calculate the following inflation-adjusted return based on the following rates: 11% rate of return, 4% inflation rate.
A)
0.36%
B)
2.75%
C)
6.73%
D)
7.00%
The answer is 6.73%.
[(1.11 ÷ 1.04) ‒ 1] × 100 = 6.7308 (6.73, rounded)
Note: Alternate calculation for this problem would be 1.04, INPUT 1.11, DOWNSHIFT, % CHG
Solve for I/YR = 6.73%
LO 4.2.2
Joe is considering purchasing a machine that will cost $10,000 to use in his business. He anticipates selling this machine at the end of five years for $3,500. The machine is projected to produce the following cash flows:
End of year 1: $300
End of year 2: $600
End of year 3: $1,200
End of year 4: $2,400
End of year 5: $4,800
Calculate the net present value (NPV) of purchasing the machine if Joe’s opportunity cost is 12%.
A)
+$2,800.00
B)
−$2,377.59
C)
−$2,164.80
D)
+$1,700.00
The answer is ‒$2,164.80.
END Mode
1, DOWNSHIFT, P/YR
C ALL
10,000, +/−, CFj
300, CFj
600, CFj
1,200, CFj
2,400, CFj
8,300, CFj
12, I/YR
DOWNSHIFT, NPV = –2,164.8039, or −$2,164.80 rounded.
LO 4.3.2
Calculate the number of months it will take $10,000 to grow to $1,000,000, assuming an annual rate of return of 6%, compounded monthly (rounded to two decimal places).
A)
923.33
B)
79.03
C)
309.31
D)
155.80
The answer is 923.33.
END Mode
12, DOWNSHIFT, P/YR
C ALL
10,000, +/-, PV
6, I/YR
1,000,000, FV
Solve for N = 923.3347, or 923.33 rounded
LO 4.1.5
Bill and Faye want to make sure they will have enough funds available to send their daughter Olivia to college. Olivia is eight years old and will begin a four-year college program at age 20 (after working full time for two years following high school graduation). Bill and Faye estimate that they can get a 7% after-tax return on their money. Based on the current tuition and anticipated rate of inflation for education, you have projected that the total cost of attendance for Olivia is $139,690.
If Bill and Faye estimate that they can get a 7% annual after-tax return on their money, what lump sum deposit would be needed today to provide for Olivia’s education?
A)
$62,024
B)
$60,111
C)
$60,675
D)
$61,044
The answer is $62,024.
END Mode
1, DOWNSHIFT, P/YR
C ALL
12, DOWNSHIFT, N (Olivia is 12 years from college; 12 periods on display)
7, I/YR
139,690, FV
Solve for PV = -62,024.0306, or $62,024 rounded.
LO 4.2.3
Chandra’s loan payments, including principal and interest, are $750 at the end of each month. She has a 25-year note with a 12% interest rate compounded monthly. What was the amount of Chandra’s original note? (Round your answer to the nearest dollar.)
A)
$71,210
B)
$16,517
C)
$100,000
D)
$71,922
The answer is $71,210.
END Mode
12, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
-750, PMT
25, DOWNSHIFT, N
12, I/YR
Solve for PV = 71,210 or $71,210
LO 4.1.3
Maria plans to purchase a condo in five years. She wants to accumulate $40,000 for a down payment. If her investments have an average annual rate of return of 7%, how much should she deposit at the beginning of each of the next five years to reach her goal of $40,000?
A)
$9,117
B)
$6,501
C)
$6,956
D)
$9,756
The answer is $6,501.
BEG Mode
1, DOWNSHIFT, P/YR
C ALL
40,000, FV
7, I/YR
5, DOWNSHIFT, N (5 periods on display)
Solve for PMT = 6,500.59, or $6,501 rounded.
LO 4.1.6
A company is considering the purchase of a copier that costs $5,000. Assume a required rate of return of 10% and the following cash flow schedule:
Year 1: $3,000
Year 2: $2,000
Year 3: $2,000
What is the project’s approximate IRR?
A)
14%
B)
10%
C)
17%
D)
21%
The IRR is 20.64%.
END Mode
1, DOWNSHIFT, P/YR
C ALL
5,000, +/‒, CFj
3,000, CFj
2,000, CFj
2,000, CFj; DOWNSHIFT, IRR/YR = 20.6402, or 21% rounded.
LO 4.3.1
Sarah wants to give her daughter $25,000 in eight years to start her own business. How much should she invest today at an interest rate of 8% compounded annually to reach her goal?
A)
$13,348
B)
$13,210
C)
$13,507
D)
$12,803
The answer is $13,507.
END Mode
1, DOWNSHIFT, P/YR
C ALL
25,000, FV
8, I/YR
8, DOWNSHIFT, N (8 periods on display)
Solve for PV = −13,506.7221, or $13,507 rounded.
LO 4.1.3
Which components of the FICO credit score calculation have the greatest impact on the total score?
Credit mix
Payment history
Amounts owed
Length of credit history
A)
II and V
B)
III and IV
C)
II and III
D)
I and II
The answer is II and III. Payment history and amounts owed have the greatest impact on total score of the FICO credit score calculation.
LO 3.3.3
Your client, Andy, is in need of assistance in preparing his statement of financial position and statement of cash flows. He earns $150,000 annually and pays $1,000 monthly in alimony to his ex-wife, Debbie. Andy owns a condo valued at $230,000, which currently has an outstanding mortgage balance of $100,000. He pays annual property taxes of $3,000, and the condo insurance costs $180 per month. All of the following statements are CORRECT except
A)
Andy’s salary would be considered a cash inflow on his statement of cash flows.
B)
the alimony Andy pays would be a cash inflow on Debbie’s statement of cash flows.
C)
taxes paid on his property would be a liability on his statement of financial position.
D)
the condo insurance payments would be a fixed outflow on Andy’s statement of cash flows.
The answer is taxes paid on his property would be a liability on his statement of financial position. The property taxes Andy pays would be considered a fixed outflow on his statement of cash flows. Such tax payments would not be an entry on a statement of financial position.
LO 3.1.2
Before any of the transactions below, Sid had a net worth of $200,000.
Took out a $24,000 loan to pay for a European vacation
Paid off his student loan of $8,000 using funds from his money market deposit account
Purchased an antique car valued at $18,000 for $15,000 with checking account funds
What is Sid’s net worth after these transactions?
A)
$186,000
B)
$173,000
C)
$179,000
D)
$169,000
The answer is $179,000. Sid’s $24,000 loan for travel increases his liabilities and does not affect his assets. Payment of his student loan will reduce debt by $8,000. However, the use of his money market deposit account to pay off the debt will reduce his assets by $8,000. The net effect of this transaction on his net worth is zero. Purchasing the antique car for $15,000 with funds from his checking account decreases assets by $15,000; however, assets are increased by $18,000 (the value of the car) for a net asset increase of $3,000. Therefore, after the transactions, his net worth decreases to $179,000 ($200,000 – $24,000 + $3,000).
LO 3.1.1
Which of these are reasons a client should consider purchasing a home rather than renting one?
Mortgage interest is generally income tax deductible
Adequate liquid assets are available for a down payment
Client plans to live in the home five years or longer
A)
I and III
B)
I, II, and III
C)
I only
D)
II and III
The answer is I, II, and III. The deductibility of mortgage interest when a client itemizes deductions is a definite tax advantage in purchasing a home as opposed to renting one. If clients intend to live in their residences for several years (more than five) and have enough money for a down payment (without depleting the emergency fund), they should consider purchasing a home.
LO 3.3.4
Which of the following statements regarding a client’s credit score is CORRECT?
Using a high percentage of available credit will positively affect a credit score.
Considering a client’s credit history only, the longer the history, the higher credit score.
A)
I only
B)
II only
C)
Both I and II
D)
Neither I nor II
The answer is II only. When considering a client’s credit history and no other FICO categories, in general, the longer the credit history, the higher the credit score. Using a high percentage of available credit will negatively affect a client’s credit score.
LO 3.3.1
Which of the following financial statements provides a snapshot of a client’s net worth at any given point in time, usually at the end of a calendar year?
Statement of cash flows
Statement of financial position
Personal tax return
Net worth statement
A)
I and IV
B)
II and IV
C)
II only
D)
II and III
The answer is II and IV. The statement of financial position, also known as a personal balance sheet or net worth statement, provides a snapshot of the client’s net worth (wealth) at any given point in time.
LO 3.1.1
What is the appropriate date to identify the statement of financial position of a calendar-year client for the year 2022?
A)
For the period from January 1 to December 31, 2022
B)
On December 31, 2022
C)
For the period beginning January 1, 2022
D)
On January 1, 2023
The answer is on December 31, 2022. The statement of financial position (personal balance sheet) is presented as of a specific date in time (i.e., a snapshot). The answer choice “For the period beginning January 1, 2022” could be correct, but the question specified the date was for a calendar-year client.
LO 3.1.1
What assets should typically NOT be used to establish an emergency fund?
A)
U.S. government bonds
B)
Cash in a basement safe
C)
Checking accounts
D)
A money market deposit account
The answer is U.S. government bonds. Bonds are not as liquid as other assets and are therefore not typically a good source of emergency funds. Money market deposit accounts are a good source for emergency funds. To the extent that they exceed the regular expenses of the client, checking account balances can be a good source for emergency funds.
LO 3.2.2
Which of the following statements regarding a client’s credit score is CORRECT?
Too many credit inquiries may lower a credit score, but likely not by much.
Opening several new accounts in a short amount of time reflects a good use of credit and therefore can increase a credit score.
A)
II only
B)
Neither I nor II
C)
Both I and II
D)
I only
The answer is I only. Opening several new accounts over a short period can lower, not increase, a client’s credit score. Too many credit inquiries may lower a client’s credit score but will likely not have a great impact.
LO 3.3.1
Which of these is characteristic of the snowball technique of debt reduction?
The debt with the lowest balance is eliminated first.
Clients are encouraged by paying off the first debt quickly.
A)
Neither I nor II
B)
Both I and II
C)
I only
D)
II only
The answer is both I and II. The snowball technique of debt reduction involves eliminating the debt with the lowest balance first. Clients are often encouraged by paying off the first debt quickly, which motivates them to continue the process.
LO 3.3.2
Joe and Mary believe in stress management. Several times each year, they take a short vacation to relax and recharge as part of their overall approach to maintaining good health. Their regularly planned vacations are an example of what type of expense?
A)
Fixed discretionary expense
B)
Variable discretionary expense
C)
Fixed nondiscretionary expense
D)
Variable nondiscretionary expense
The answer is variable discretionary expense. Although Joe and Mary believe the vacations to be important for good health, the vacations are considered a variable discretionary expense.
LO 3.1.2
Which of the following statements regarding liabilities on the statement of financial position is CORRECT?
They are categorized as fixed or variable.
Any outstanding mortgage balance is reported as its original amount.
A)
II only
B)
Both I and II
C)
Neither I nor II
D)
I only
The answer is neither I nor II. Liabilities are categorized as current (short-term) liabilities or long-term on the statement of financial position. The current outstanding mortgage balance as of the date of the statement of financial position, not the original mortgage amount, is reported on this statement.
LO 3.1.1
Which of these types of accounts are covered by Federal Deposit Insurance Corporation (FDIC) insurance?
Securities
Certificates of deposit
Money market mutual funds
Money market deposit accounts
A)
II, III, and IV
B)
II and IV
C)
III and IV
D)
I, II, and III
The answer is II and IV. Certificates of deposit are afforded FDIC protection; securities are not. Money market deposit accounts, not money market mutual funds, are covered by FDIC insurance.
LO 3.4.1
Which components of the FICO credit score calculation have the greatest impact on the total score?
New credit
Length of credit history
Amounts owed
Payment history
A)
I and III
B)
II and IV
C)
I and IV
D)
III and IV
The answer is III and IV. Payment history (35% of credit score) and amounts owed (30% of credit score) have the greatest impacts on the total FICO score.
LO 3.3.1
Allyson would like to pay off her debt, reducing the debt with the highest interest rate first. Compared to the snowball approach of debt reduction, which of the following statements are CORRECT?
Compared to the snowball approach, it is relatively more difficult to pay off the first debt with a high balance quickly.
This approach increases the total amount of interest paid during the debt reduction process.
A)
Both I and II
B)
II only
C)
I only
D)
Neither I nor II
The answer is I only. With Allyson’s approach, it often takes longer to pay off the first debt when the highest interest rate has a considerable balance. Less interest paid during the debt reduction process is an advantage of paying off debt in order of interest rate.
LO 3.3.2
All of the following items should be included on an individual’s statement of financial position except
A)
fair market value of a home.
B)
mortgage balance.
C)
mortgage payment.
D)
mutual fund balance.
The answer is mortgage payment. The mortgage payment, which is considered a fixed outflow, is included on the statement of cash flows, not the statement of financial position. The mortgage balance should be shown as a liability on the statement of financial position. The fair market value of a home and the balance of a mutual fund should be listed as assets on the statement of financial position.
LO 3.1.1
Which of the following actions would most likely decrease an individual’s credit score?
A)
Make just the minimum payment on time each month
B)
Take advantage of several offers for new credit cards
C)
Pay off a balance on a credit card that the individual has had for 10 years
D)
Have several different types of credit accounts, such as a car loan, a mortgage, and credit cards
The answer is take advantage of several offers for new credit cards. Taking advantage of several offers for new credit cards would decrease an individual’s credit score.
LO 3.3.3
Doug has the following amounts on deposit at the same bank.
Account Ownership Balance
Savings account Doug $200,000
Traditional IRA Doug $300,000
Certificate of Deposit Joint with spouse $400,000
How much Federal Deposit Insurance Corporation (FDIC) insurance coverage does Doug have for his accounts at the bank?
A)
$650,000
B)
$450,000
C)
$900,000
D)
$700,000
The answer is $650,000. Each category of ownership (e.g., individual, joint, or retirement account) in the same institution is subject to a separate limit of $250,000. Doug has $200,000 of coverage on his individual savings account, $250,000 of coverage on the traditional IRA, and $200,000 of coverage on the joint account, for a total of $650,000.
LO 3.4.1
Alex has a personal emergency requiring him to immediately access $50,000. He expects this need will last for several months. Which of the following assets shown on his statement of financial position is the best choice to pay for his emergency?
A)
A life insurance cash surrender value in the amount of $55,000
B)
A money market mutual fund worth $35,000
C)
A credit union account totaling $60,000
D)
Aggressive stocks currently trading at a market value of $65,000
The answer is a credit union account totaling $60,000. Although both the credit union account and the money market mutual fund reflect liquid assets, the best asset to use is the credit union account because it sufficiently covers Alex’s needs.
LO 3.2.2
Which of the following items should NOT be included in an individual’s statement of cash flows?
Home value
Mortgage balance
Mortgage payment
Mutual fund balance
A)
I, II, and IV
B)
III only
C)
I and IV
D)
I and II
The answer is I, II, and IV. The mortgage balance should be shown as a liability on the statement of financial position. The value of a home and the balance of a mutual fund should be listed as assets on the statement of financial position. Only the mortgage payment, which is considered a fixed outflow, is included in the statement of cash flows.
LO 3.1.2
What is the key to successfully using the snowball technique to eliminate debt?
A)
Developing a plan that the client can commit to executing
B)
Start with the debt that has the highest account balance
C)
Begin with the debt that has the highest interest rate
D)
Begin with the debt that has the highest payment
The answer is developing a plan that the client can commit to executing. The key to the effectiveness of using the snowball technique is developing a plan that the client can commit to and execute. The goal is eliminating debt, and the client needs to agree to the process to make that happen. Beginning a debt reduction plan with the debt that has the highest payment is not a typical debt reduction technique.
LO 3.3.2
Which of these statements regarding credit unions are CORRECT?
Loans are typically offered at reduced interest rates.
Earnings from loan interest and investments are paid to members in the form of shares.
Deposits in a credit union are insured up to $100,000 per qualifying account by the National Credit Union Share Insurance Fund (NCUSIF).
Each credit union member may use a vote to elect the board of directors.
A)
I and IV
B)
III and IV
C)
II and IV
D)
I, II, and III
The answer is I and IV. Statement II is not correct because earnings from loan interest and investments are paid to members in the form of dividends, not shares. Statement III is not correct because deposits in a credit union are insured up to $250,000 per qualifying account by the NCUSIF.
LO 3.4.2
Some rule-of-thumb ratios are helpful in understanding how a client’s debt will be assessed by lenders, which can determine interest rates. Which of these is NOT correct regarding ratio descriptions and the related benchmark?
A)
The minimum required payments should be used in the calculation.
B)
Consumer debt is all nonmortgage debt. It should be no more than 20% of monthly net income.
C)
Total monthly payment on all debts should be no more than 36% of gross monthly income.
D)
Monthly housing costs include principal, interest, taxes, fees, and insurance, and should be no more than 28% of the prospective borrower’s net income.
Monthly housing costs include principal, interest, taxes, fees, and insurance, and should be no more than 36% of the prospective borrower’s net income. Keeping all debt payments under 36% is important in order to qualify for reasonable rates on credit. Helping clients understand what will make future debt more costly can give them motivation to stay within the guidelines. Monthly housing costs should be no more than 28% of the prospective borrower’s gross, not net, income.
LO 3.1.3
Which of the following has the least impact on a client’s total FICO score?
A)
Credit mix
B)
Amounts owed
C)
Length of credit history
D)
Payment history
The answer is credit mix. These categories affect credit scores in the following percentages: credit mix, 10%; length of credit history, 15%; amounts owed, 30%; and payment history, 35%
LO 3.3.1
Which of the following statements regarding the identification of financial strengths and weaknesses is CORRECT?
This process is primarily subjective.
A planner may rely on financial ratios to assist in making this determination.
A)
Neither I nor II
B)
Both I and II
C)
II only
D)
I only
The answer is both I and II. During this subjective process, a planner may rely on financial ratios to assist in identifying financial strengths and weaknesses.
LO 3.1.4
Brandon and Jessica are in their mid-30s. Both are employed and they have no children. They enjoy international travel and own luxury automobiles. To afford their lifestyle, the couple has accumulated significant debt. In addition to their large car loans, Brandon and Jessica have balances on multiple credit cards and a substantial private loan used to pay for a Mediterranean cruise. Within the next few months, they intend to purchase a home. Both Brandon and Jessica are aware of their need to plan for retirement, but their current debt makes it difficult for them to consistently save money. After meeting with the couple and analyzing their financial statements, you recommend they adopt a savings plan. Assuming they accept your recommendation, which of the following steps would help Brandon and Jessica maximize their savings potential?
Begin paying off their debts, giving priority to the debt with the highest interest rate
Monitor their spending to ensure they are not using debt to finance a lifestyle they cannot afford
A)
II only
B)
I only
C)
Both I and II
D)
Neither I nor II
The answer is both I and II. Both of these steps should be implemented as part of the Brandon and Jessica’s savings plan.
LO 3.2.3
When preparing a cash flow statement for a client, what is the CORRECT way to indicate the period covered?
A)
For the period January 1, 20XX to December 31, 20XX
B)
As of December 31, 20XX
C)
For the period January to December 20XX
D)
From January 20XX to December 20XX
The answer is for the period January 1, 20XX to December 31, 20XX. Usually the cash flow statement is prepared for the calendar year period, specifying the dates.
LO 3.1.2
Jake and Ashley are working with their financial planner to develop a budget. The financial planner told them to list all their fixed cash outflows and variable cash outflows on a questionnaire. Which of the following would be considered a fixed cash outflow for planning purposes?
A)
Food
B)
Mortgage payments
C)
Travel and entertainment
D)
Utilities
The answer is mortgage payments. Only mortgage payments are considered a fixed cash outflow. Other examples of fixed cash outflows are car payments, insurance premiums, and property taxes.
LO 3.2.1
Which of the following statements regarding the identification of financial strengths and weaknesses is CORRECT?
This process is primarily objective.
A planner may rely on financial ratios to assist in making this determination.
A)
Both I and II
B)
I only
C)
Neither I nor II
D)
II only
The answer is II only. Although a planner may rely on financial ratios to assist in identifying financial strengths and weaknesses, this analysis is generally subjective.
LO 3.1.4
Which of these are tax implications of owning a personal residence?
The points paid are tax deductible for the buyer
Mortgage interest is generally tax deductible for the buyer
Capital gains may be nontaxable within specific limits
Homeowners may depreciate their personal residence
A)
I, II, and III
B)
II and III
C)
I and III
D)
I, II, and IV
The answer is I, II, and III. Although I, II, and III are tax implications of home ownership, exceptions and restrictions apply to these benefits. A taxpayer of any age can exclude $250,000 of gain ($500,000 for joint filers) from the sale of a home owned and used by the taxpayer as a principal residence for at least two of the five years immediately preceding the sale. Generally, an individual cannot claim depreciation on a personal residence.
LO 3.3.4
