Module 4 Flashcards
1
Q
Compounding
A
The process of interest being earned on increasing sums of principal and interest over time.
2
Q
Carlos received $13,000 from an inheritance, and he wants to invest it for the next 11 years. If he can earn 7.5% annually after tax, how much will his account be worth at the end of 11 years?
A
The account is worth $28,803, with keystrokes as follows:
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
13,000, +/–, PV
11, N
7.5, I/YR
Solve for FV = 28,802.9160 or $28,803
3
Q
Annuity
A
If the payments are equal and regular, the series of savings deposits or payments is called (in time value of money language) an annuity.
4
Q
Future Value of an Annuity
A
The accumulation of funds needed to meet a future financial goal.
5
Q
Annuity Due
A
If each of the payments are made at the beginning of each period (e.g., as with lease payments), the series of payments is known as an annuity due.
6
Q
Ordinary Annuity
A
If each payment is made at the end of each period (e.g., as with mortgage payments), the series is known as an ordinary annuity.
7
Q
Hector has been investing $2,000 at the end of each year for the past 18 years in a growth mutual fund. How much is the fund worth now assuming he has earned 10% compounded annually on his investment?
A
The fund is worth $91,198, with keystrokes as follows:
END mode (just take off BEG mode as the calculator is pre-programed to be in END mode)
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
2,000, +/–, PMT (Note: This is a cash outflow from the client; therefore, enter it as a negative amount.)
10, I/YR
18, N
Solve for FV = 91,198.3463, or $91,198
8
Q
With respect to calculator entry, whenever you are solving for the future value (FV) of an annuity, which key must be used?
A
The payment (PMT) key.
9
Q
As with the FV process, the PV of a single amount depends on the:
A
length of time before the single amount will be received and
annual (or some other time period, such as monthly [×12], semiannually [×2], or quarterly [×4]) interest rate or rate of return.
10
Q
Kali needs a total of $100,000 in 10 years to pay for four years of college for her granddaughter. If she can earn 7.5% annually after tax on her growth mutual fund set aside for this purpose, what single amount must Kali invest today?
A
Kali needs to invest $48,519, with keystrokes as follows:
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
100,000, FV
10, N
7.5, I/YR
Solve for PV = −48,519.3928, or $48,519 (Note: The HP10bII/ HP10bII+ calculator will return a negative number in this case. The negative sign displayed before the PV amount indicates that this investment is a cash outflow to Kali.)
11
Q
Nick’s grandmother plans on giving him $5,000 at the end of each year for the next five years. Assuming a discount rate of 4%, what is the PV of this sum?
A
The PV is $22,259, with keystrokes as follows:
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
5,000, +/−, PMT
4, I/YR
5, N
Solve for PV = 22,259.1117, or $22,259
12
Q
Nick’s grandmother plans on giving him $5,000 at the beginning of each year for the next five years. Assuming a discount rate of 4%, what is the PV of this sum?
A
The PV is $23,149, with the keystrokes as follows:
BEG mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
5,000 PMT
4 I/YR
5 N
Solve for PV = 23,149.4761, or $23,149
13
Q
Halia invests $1,000 today with the hope that in five years her investment will be worth $1,500. The investment will compound semiannually. At the end of five years, what will be the rate of return?
A
The I/YR is 8.28%, with keystrokes follows:
END mode
2, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
1,000, +/–, PV
1,500, FV
5, DOWNSHIFT, xP/YR (10 should appear on display)
Solve for I/YR = 8.2760, or 8.28%
14
Q
If you change P/YR to an amount other than 1 (annual), you should:
A
enter the number of years, followed by “DOWNSHIFT, xP/YR”.
15
Q
Rule of 72
A
To calculate the number of years for an investment to double in value, simply divide 72 by the annual interest rate. For example, if the client’s objective is to double a $1,000 investment that is earning a compound annual rate of return of 9%, it will take approximately eight years (72 ÷ 9 = 8). Alternatively, if the investor wants to double his original investment in 10 years, divide 72 by 10 to derive an approximate required annual interest rate of 7.2%.
16
Q
Angela has an IRA with a current balance of $4,000. How many years will it take for this account to grow to $20,000 at a 12% annual rate of return?
A
The answer is 14.2 years with keystrokes as follows:
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
4,000, +/−, PV
20,000, FV
12, I/YR
Solve for N = 14.2015, or 14.2 years
17
Q
Erica and Tyler would like to accumulate $50,000 for a down payment on a new home. If they are able to save $500 at the end of each month and these funds earn 10% per year, how many years will it take for the couple to accumulate the needed $50,000?
A
The answer is 6.09 years with keystrokes as follows:
END mode
12, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
50,000, FV
500, +/−, PMT
10, I/YR
Solve for N = 73.0389 months, or 73.03 ÷ 12 = 6.09 years
18
Q
Fixed (equal) Payments
A
Unchanging payments over the entire period.
19
Q
Serial Payments
A
Payments increase each year by the amount of inflation (to maintain a constant or real dollar amount).
20
Q
Amul purchases a new car and finances $21,000 with a 5.9% loan over three years. Assuming each payment is due at the end of the month, what is the amount of Amul’s monthly car payment?
A
Amul’s car payment is $637.91, with keystrokes as follows:
END mode
12, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
21,000, PV
5.9, I/YR
3, DOWNSHIFT, xP/YR (36 should appear on display)
Solve for PMT = −637.9096, or $637.91 (Note: Because the PMT is a cash outflow for Amul, it is displayed as a negative number.)
21
Q
Loan amortizations (e.g., mortgages, auto loans) are calculated using what mode?
A
END mode because the interest on the principal balance is accruing from payment to payment on the balance of the debt.
22
Q
Amortization
A
Refers to the repayment of loan principal over time.
23
Q
Amortization Schedule
A
Refers to how much principal and how much interest is being repaid with each payment.
24
Q
Sarah and Sean have finalized a $135,000, 30-year loan with a 4.5% interest rate. What are the keystrokes for the mortgage amortization calculation?
A
END mode
12, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
135,000, PV
4.5, I/YR
30, DOWNSHIFT, xP/YR (360 should appear on display)
Solve for PMT = −684.0252, or $684.03
25
Jack is buying a new car for $30,000 with a down payment of $2,000, and he is financing the balance of $28,000 with a five-year, 3.25% loan. What is Jack’s monthly payment, and how much interest will he pay over the life of the loan?
END mode
12, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
28,000, PV
3.25, I/YR
5, DOWNSHIFT, xP/YR (60 should appear on display)
Solve for PMT = −506.2401, or $506.24
1, INPUT, 60
DOWNSHIFT, AMORT
= (−28,000.23 appears on display, represents principal paid)
= (−2,374.4037 appears on display, represents interest paid)
= (−0.0023 appears on display, represents remaining balance, off by 0.0023 due to rounding)
26
Jack is considering purchasing a car from another dealer and would be borrowing $18,000 for five years with a monthly payment of $341.75. What interest rate is he being charged?
END mode
12, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
18,000, PV
341.75, +/−, PMT
5, DOWNSHIFT, xP/YR (60 should appear on display)
Solve for I/YR = 5.2503, or 5.25%
27
What is the equation for inflation-adjusted interest rates?
[(1 + rate of return) / (1 + rate of inflation)] -1] x 100
28
What would the inflation-adjusted interest rate be with a 7% rate of return and a 3% inflation rate?
1.07/1.03 = 1.038835
(1.038835 - 1) x 100 = 3.88%
OR
1.03, INPUT
1.07, DOWNSHIFT, % CHG
Solve for I/YR = 3.88% (rounded)
29
Assume Carly wants to save $50,000 (in today’s dollars) for her son’s college expenses in five years. Carly is comfortable using an inflation rate of 4% and an investment rate of return of 8%. How much does she need to save the first year?
She needs to save $9,630.17 in the first year, calculated as follows:
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
50,000 FV
5 N
[(1.08 ÷ 1.04) − 1] × 100 = 3.8462, I/YR
Solve for PMT = −9,259.7738, or $9,259.77
Because the payments are made at the end of each year, the calculated payment of $9,259.77 must be inflated by 4%. Therefore, to calculate the end of the first year payment, multiply $9,259.77 by 1 + the inflation rate, or 1.04. This results in an end-of-year payment of $9,630.16. All five payments are as follows:
$9,259.77 × 1.04 = $9,630.16
$9,630.16 × 1.04 = $10,015.37
$10,015.37 × 1.04 = $10,415.99
$10,415.99 × 1.04 = $10,832.62
$10,832.62 × 1.04 = $11,265.93
30
An investor makes an initial deposit of $20,000 into a mutual fund. Each subsequent year, he deposits an additional $2,500 into the fund. What will be the value of the account in eight years if the fund earns 9% annually?
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
8, N
9, I/YR
20,000, +/−, PV
2,500, +/−, PMT
Solve for FV = $67,422.4373, or $67,422.44
The account value after eight years would be $67,422.44.
31
A client would like to accumulate $300,000 for retirement, which will begin in 10 years. She can invest $10,000 at the end of each year toward this goal in an account earning 8% annually. What initial lump-sum deposit, in addition to the payment stream, is required for her to be able to meet this goal?
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
10, N
8, I/YR
300,000, FV
10,000, +/−, PMT
Solve for PV = −71,857.2324, or $71,857.23
The initial deposit required to meet the client’s goal is $71,857.23
32
Enrique and Sofia would like to purchase a home in five years and need $30,000 for the down payment. They can save $3,600 at the end of each year and can get a 5% return on the investment account they are using. What lump sum do they need, in addition to their annual savings, to reach their goal?
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
5, N
5, I/YR
30,000, FV
3,600, +/−, PMT
Solve for PV = −7,919.6690, or $7,919.67
The initial deposit required to meet the client’s goal is $7,919.67.
33
Felix wants to save $125,000 to achieve a future goal. He has $26,000 to invest currently and can invest $10,000 at the end of each year toward his goal. If the investment vehicle selected earns 10% annually, how many years will it take to achieve Felix’s goal?
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
10, I/YR
26,000, +/−, PV
10,000, +/−, PMT
125,000, FV
Solve for N = 6.0835, or 6.08
It will take just over six years (6.08 years) for the client to achieve his goal.
Note that when you solve for N you are solving for number of compounding periods, not necessarily number of years. If there is annual compounding (as there is in this example), then the number of compounding periods and number of years will be the same. For more frequent compounding, you will need to divide by the number of compounding periods per year to calculate the number of years it would take to reach a goal.
34
Dante wants to save $125,000 to achieve a future goal. He has $26,000 to invest currently and can invest $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 Dante’s goal?
END mode
4, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
10, I/YR
26,000, +/−, PV
2,500, +/−, PMT
125,000, FV
Solve for N = 23.4815
This means that it will take 23.4815 compounding periods to reach Dante’s goal. To express this in years, divide 23.4815 by 4 (number of compounding periods per year), which equals 5.87 years.
35
Shaila 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 Shaila’s goal?
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
11, I/YR
32,000, +/−, PV
90,000, FV
7, N
Solve for PMT = −2,408.4856, or $2,408.49
The periodic payment required each year is $2,408.49.
36
Six years ago, Theo invested $5,000 in a mutual fund. He made additional investments of $300 at the end of each year. Yesterday, Theo redeemed all fund shares and received $8,500. What was the rate of return on his investment?
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
5,000, +/−, PV
8,500, FV
300, +/−, PMT
6, N
Solve for I/YR = 4.4378, or 4.44%
The rate of return has been 4.44% annually.
37
Internal Rate of Return (IRR)
Rate of growth that an investment is expected to generate.
38
If NPV is being calculated, CF0 is input as:
A zero.
39
What is the average compound rate of return that has been earned from investing in an antique chair that was purchased six years ago for $1,000, was repaired at the end of the second year at a cost of $450, and has just sold for $2,850?
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
1,000, +/−, CFj
0, CFj
450, +/−, CFj
0, CFj
0, CFj
0, CFj
2,850, CFj
DOWNSHIFT, IRR/YR = 13.2502, or 13.25%
OR
END mode
1 DOWNSHIFT P/YR
DOWNSHIFT C ALL
1,000, +/−, CFj
0, CFj
450, +/−, CFj
0, CFj
3, DOWNSHIFT, Nj
2,850, CFj
DOWNSHIFT, IRR/YR = 13.2502, or 13.25%
IRR (average compound rate of return) is 13.25%.
40
A three-year investment in a mutual fund pays the following quarterly distributions: four distributions at $500, four at $570, and four at $600. These distributions are not reinvested back into the fund. The initial investment into the fund was $120,000, and the final value of the mutual fund account at the time of the last quarterly distribution was $165,000. What is the IRR earned?
END mode
4 DOWNSHIFT P/YR
DOWNSHIFT C ALL
120,000, +/−, CFj
500, CFj
4, DOWNSHIFT, Nj
570, CFj
4, DOWNSHIFT, Nj
600, CFj
3, DOWNSHIFT, Nj
165,600, CFj
DOWNSHIFT, IRR/YR = 12.3577, or 12.36% The IRR is 12.36%.
NOTE!: Notice the last two entries that are listed. The $600 quarterly distribution is entered three times, and then the last $600 is added to the amount that is $. This is a common mistake made by students. If you were to enter $600 four times, then the investment would have been held for three years and one quarter. That is why we need to add the last quarterly distribution to the amount being returned.
41
PV of Cash Flows - Cost of Investment = ?
NPV of investment.
42
If the NPV is positive, it means that the investment would:
Earn a return more than the discount rate (required rate of return).
43
If the NPV is negative, it means the investment would:
Earn a return less than the discount rate.
44
A real estate property being offered for $500,000 is expected to have cash flows of $30,000, $35,000, and $40,000 over each year in the following three-year period, respectively. At the end of three years, it is expected to have a value of $575,000. (Note that the last cash flow will be $40,000 + $575,000 = $615,000.)
If an investor has a required rate of return of 10%, what is the PV and NPV of the property?
END mode
1 DOWNSHIFT P/YR
DOWNSHIFT C ALL
0, CFj
30,000, CFj
35,000, CFj
615,000, CFj
10, I/YR
DOWNSHIFT, NPV = 518,256.9497, or $518,256.95
The PV (the price) that will allow a 10% return on the investment is $518,256.95. In other words, if the investor paid this amount and received the assumed cash flows, they would achieve a 10% return.
$518,257 (PV) - $500,000 (Initial Investment) = $18,257 (NPV)
Because the NPV is positive, it means that if the investor paid $500,000, the IRR for the property would be higher than the discount rate (required return) of 10%. Actually, the return is 11.40%.
END mode
1 DOWNSHIFT P/YR
DOWNSHIFT C ALL
500,000, +/−, CFj
30,000, CFj
35,000, CFj
615,000, CFj
DOWNSHIFT, IRR/YR = 11.3992, or 11.40%
45
What is the PV of an investment for which the following cash flows are expected, assuming that the client’s required compound rate of return for an investment at this level of risk is 8%?
END mode
1 DOWNSHIFT P/YR
DOWNSHIFT C ALL
0, CFj
1,000, CFj
500, +/−, CFj, 3 DOWNSHIFT, Nj
0, CFj
3,000, CFj
8, I/YR
DOWNSHIFT, NPV = 1,623.3343, or $1,623.33
The PV, or the price, that will allow an 8% return on this investment is $1,623.33. In other words, if you invested $1,623.33 today and received the cash flows indicated in the table over the six years subsequent to making the investment, you would achieve an 8% compound return. If you invest more than $1,623.33, you will receive a compound return of less than 8%; and if you invest less than $1,623.33, you will receive a compound return of more than 8%.
46
Danielle has $150,000 in her Section 401(k) plan portfolio at work. She expects the portfolio to increase in value at a rate of 7% compounded annually for the next five years. Calculate the value of Danielle’s portfolio at the end of five years, assuming her expectations are accurate.
$210,383
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
150,000, +/–, PV
5, N
7, I/YR
Solve for FV = $210,382.7596, or $210,383
47
Taj invested $20,000 in an account earning a 9% annual rate of interest compounded monthly. Calculate his account value at the end of eight years if all interest is reinvested at the 9% rate.
$40,978
END mode
12, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
20,000, +/−, PV
8, DOWNSHIFT, xP/YR
9, I/YR
Solve for FV = $40,978.4246, or $40,978
48
Steve has been investing $5,000 at the beginning of each year for the past 20 years. Assuming he has earned 11% compounded annually on his investment, calculate the amount Steve has accumulated.
$356,326
BEG mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
5,000, +/−, PMT
20, N
11, I/YR
Solve for FV = $356,325.7184, or $356,326
49
Roxanne has already saved $5,000 for a down payment on a future house. She adds $2,000 at the end of every year into an account earning an annual rate of 5.5% compounded annually. Calculate the amount Roxanne will have accumulated in four years.
$14,879
END mode
2, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
5,000, +/−, PV
2,000, +/−, PMT
4, DOWNSHIFT, xP/YR (8 should appear on display)
5.5, I/YR
Solve for FV = 14,878.6560, or $14,879
50
Mary wants to give her daughter $200,000 to start her own business in five years. Calculate the amount she should invest today at an annual interest rate of 9% compounded annually to have $200,000 in five years.
$129,986
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
200,000 FV
5, N
9. I/YR
Solve for PV = $129,986.2773, or $129,986
51
Sam wants to accumulate $75,000 in 7.5 years to purchase a boat. He expects to earn an annual rate of return on invested funds of 12% compounded quarterly. How much does Sam need to invest today to meet his goal?
$30,899
END mode
4, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
75,000 FV
7.5, DOWNSHIFT, xP/YR (30 should appear on display)
12, I/YR
Solve for PV = −30,899.0070, or $30,899
52
Nathan borrowed $800 from his father to purchase a new jet ski. He plans to pay $1,200 back to his father after five years. Calculate the anticipated average annual compound rate of interest that Nathan’s father will receive.
8.45%
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
800, +/−, PV
1,200, FV
5, N
Solve for I/YR = 8.4472, or 8.45%
53
Hiro contributes to his retirement account at the end of each quarter. He has $60,000 in current savings and wants to reach an account balance of $100,000 in the next six years. Hiro’s investments will earn an annual rate of return of 7% compounded quarterly. Calculate the amount that he needs to contribute each quarter.
$305.43
END mode
4, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
100,000, FV
60,000, +/−, PV
7, I/YR
6, DOWNSHIFT, xP/YR (24 should appear on display)
Solve for PMT = −305,4260, or $305.43
54
Jeremiah secures a $400,000 mortgage with a 15-year repayment term and an annual interest rate of 5.25%. Calculate the monthly payment on this loan.
$3,215.51
END mode
12, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
400,000, PV
15, DOWNSHIFT, xP/YR (180 should appear on display)
5.25, I/YR
Solve for PMT = −3,215.5109, or $3,215.51
55
Jeremiah secures a $400,000 mortgage with a 15-year repayment term and an annual interest rate of 5.25%. The monthly payment on his loan is $3,215.51. Calculate the balance of Jeremiah’s mortgage at the end of 1 year (12 payments).
$381,984.47
END mode
12, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
400,000, PV
15, DOWNSHIFT, xP/YR (180 should appear on display)
5.25, I/YR
Solve for PMT = −3,215.5109, or $3,215.51
1 INPUT 12
DOWNSHIFT, AMORT
= −18,015.5294 total principal paid through 12 months
= −20,570.6014 total interest paid through 12 months
= 381,984.4706 remaining mortgage balance through 12 months
56
Calculate the following inflation-adjusted returns:
- 7% rate of return, 2.5% inflation rate
- 11% rate of return, 4% inflation rate
- 4.5% rate of return, 2% inflation rate
- 4.39%
- 6.73%
- 2.45%
57
Gemma wants to receive the equivalent of $30,000 in today’s dollars at the beginning of each year for the next seven years. She assumes that inflation will average 4% over the long run and that she can earn a 9% compound annual after-tax return on investments. What lump sum does Gemma need to invest today to achieve her goal?
$183,211.73
BEG mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
7, N
[(1.09 ÷ 1.04) − 1] × 100 = 4.8077, I/YR
30,000, PMT
Solve for PV = −$183,211.73, or $183,211.73
58
In considering his life insurance needs, Archie has determined that, in the event of his death, his dependents will need $28,800 in today’s dollars at the beginning of each year. This payment will be needed until his youngest child reaches age 18, which is 15 years from now. If he assumes an inflation rate of 5% and an after-tax yield of 8%, what is the PV of these payments?
$357,317.71
BEG mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
15, N
[(1.08 ÷ 1.05) – 1] × 100 = 2.8571, I/YR
28,800, PMT
Solve for PV = –$357,317.7092, or $357,317.71
59
Cynthia has just invested $5,000 into a stock index fund in her IRA and intends to deposit an additional $200 at the end of each month going forward. Calculate what her IRA account would be worth after 15 years of investing if she earns an average annual rate of return of 9%.
$94,871.37
END mode
12, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
5,000, +/−, PV
200, +/−, PMT
15, DOWNSHIFT, xP/YR (180 should appear on display)
9, I/YR
Solve for FV = $94,871.3701, or $94,871.37
60
Calculate how many years it would take Cynthia to accumulate $125,000 if she were to invest $5,000 today and an additional $200 at the end of each month, while earning an average annual rate of return of 9%
17.47
END mode
12, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
5,000, +/−, PV
200, +/−, PMT
9, I/YR
125,000, FV
Solve for N = 209.6383, or 209.64 (number of compounding periods)
To convert to number of years, divide by the number of compounding periods per year: 209.64 ÷ 12 = 17.47 years
61
Yvette wants to accumulate $80,000 for a future goal in nine years. She can deposit $18,000 today and wants to know what payment she would need to make at the beginning of each six-month period to reach her goal. She is conservative with her investments and wants to assume a 3% rate of return.
$2,715.23
BEG mode
2, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
18,000, +/−, PV
3, I/YR
9, DOWNSHIFT, xP/YR (18 should appear on display)
80,000, FV
Solve for PMT = −2,715.2300, or $2,715.23
62
Eight years ago, Johnathan invested $25,000 into an energy fund and has been adding an additional $1,250 to the fund at the end of each year. The fund is currently worth $44,500. What was the rate of return on this investment?
3.59%
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
25,000, +/−, PV
1,250, +/−, PMT
8, N
44,500, FV
Solve for I/YR = 3.5897, or 3.59%
63
Drake purchased rental property four years ago for $128,900. His cash flows for each year were as follows:
Year 1: $2,800 Inflow
Year 2: $5,200 Inflow
Year 3: $7,000 Inflow
Year 4: $7,000 Inflow
If the property is worth $145,000 at the end of the fourth year, what would Drake’s IRR be?
6.99%
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
128,900, +/−, CFj
2,800, CFj (This is a positive cash flow: 6,000 inflow minus 3,200 outflow.)
5,200, CFj
7,000, CFj
152,000, CFj
DOWNSHIFT, IRR/YR = 6.9854, or 6.99%
Note that the purchase price is entered as the first cash flow (cash is purchasing property, so it would be a negative number, an outflow). Also, the final cash flow at the end of the fourth year (net inflow of $7,000) is added to the value of the property ($145,000) to calculate an end of year 4 cash flow of $152,000.
64
Zack invested $15,000 in a mutual fund six years ago, and it has had the following end-of-year distributions:
End of Year 1: $175
End of Year 2: $225
End of Year 3: $225
End of Year 4: $225
End of Year 5: $250
End of Year 6: $215
Zack redeemed $4,500 of the fund in year 5 and sold the remainder of his shares for $16,500 at the end of year 6. What is Zack’s internal rate of return (IRR)?
7.30%
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
15,000, +/−, CFj
175, CFj
225, CFj
3, DOWNSHIFT, Nj (three $225 cash flows—could also just enter each separately)
4,750, CFj ($250 distribution plus $4,500 redemption)
16,715, CFj ($215 distribution plus $16,500 redemption)
DOWNSHIFT, IRR/YR = 7.3030, or 7.30%
65
Glenda is considering the purchase of some rental property. The owner is asking $725,000, and the apartment units are expected to generate cash flows of $50,000, $55,000, $60,000, and $65,000 over the next four years. The property is expected to be worth $850,000 at the end of four years. What is the maximum amount that Glenda should pay for the property (its intrinsic value) if her required rate of return is 9%?
What is the NPV of the property?
What would Glenda’s IRR be if she were to purchase the property for $725,000 and receive the anticipated cash flows provided previously?
Max amount Glenda should pay: $786,704.04
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
0, CFj
50,000, CFj
55,000, CFj
60,000, CFj
915,000, CFj ($65,000 + $850,000)
9, I/YR
DOWNSHIFT, NPV = 786,704.0362, or $786,704.04
NPV: $61,704.04
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
725,000, +/–, CFj
50,000, CFj
55,000, CFj
60,000, CFj
915,000, CFj ($65,000 + $850,000)
9, I/YR
DOWNSHIFT, NPV = 61,704.0362, or $61,704.04
Note that the NPV is the difference between the $786,704.04 intrinsic value we calculated for the property previously, and the $725,000 asking price for the property.
Glenda's IRR: 11.47%
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
725,000, +/−, CFj
50,000, CFj
55,000, CFj
60,000, CFj
915,000, CFj
DOWNSHIFT, IRR = 11.4732, or 11.47%
66
What is the NPV of an investment that would provide the following inflows, assuming that the client’s opportunity cost is 12%?
End of Year 1: $1,200
End of Year 2: $1,500
End of Year 3: $1,800
End of Year 4: $2,200
$4,946.56
END mode
1, DOWNSHIFT, P/YR
DOWNSHIFT, C ALL
0, CFj
1,200, CFj
1,500, CFj
1,800, CFj
2,200, CFj
12, I/YR
DOWNSHIFT, NPV = 4,946.5636, or $4,946.56
67
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) $23,420.00
B) $24,122.60
C) $24,846.28
D) $25,591.67
C) $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
68
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) $1,200 per year invested annually starting one year from now
B) $100 per month invested on the first of the month, starting in 30 days
C) $100 per month invested on the first of the month, starting today
D) $1,200 per year invested annually starting today
D) $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.
69
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) $10,760,716
B) $4,627,549
C) $10,248,301
D) $10,392,100
C) $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.
70
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
A) 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
71
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) $9,364
D) $9,551
C) $9,364
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.
72
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) $28,253
B) $25,296
C) $22,657
D) $27,950
C) $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.
73
Kerry purchased an antique for $12,000. Today, he sold the antique for $69,975.49. Kerry estimated the average annual compound rate of return on the antique was 8%. Approximately how many years did Kerry own the antique (rounded to the nearest 0.00)?
A) 24.66
B) 22.91
C) 20.19
D) 22.15
B) 22.91
The answer is 22.91.
END Mode
1, DOWNSHIFT, P/YR
C ALL
8, I/YR
12,000, +/‒, PV
69,975.49, FV
Solve for N = 22.9108 (22.91, rounded)
74
Which of the following statements regarding serial payments and fixed annuity payments is CORRECT?
A) Serial payments are similar to fixed annuities in that they both pay out a fixed amount each year.
B) The last serial payment will be less than the respective fixed annuity payment.
C) A serial payment is a payment that increases at some constant rate on a regular basis.
D) The last serial payment will have less purchasing power than the first serial payment.
C) A serial payment is a payment that increases at some constant rate on a regular basis.
Serial payments differ from fixed annuity payments (both ordinary and annuity due payments) in that serial payments are not a fixed amount per year. Thus, the initial serial payment is less than its respective annuity due or ordinary annuity payment. The last serial payment will obviously be greater than the last respective fixed annuity payment but will have the same purchasing power as the first serial payment.
75
What is the end of the month payment required to accumulate a balance of $150,000 in 10 years at an assumed annual interest rate of 11% (compounded monthly) and a beginning savings balance of $2,500?
A) $691.25
B) $656.81
C) $684.97
D) $650.85
B) $656.81
The answer is $656.81.
END Mode
12. DOWNSHIFT, P/YR
C ALL
2,500, +/‒, PV
11, I/YR
10, DOWNSHIFT, N (120 shows on display)
150,000, FV
Solve for PMT = -656.8127, or $656.81
76
Pat wants to start his own business in five years. He needs to accumulate $500,000 (in today's dollars) in five years to sufficiently finance his business. He assumes inflation will average 2% and that he can earn a 6% (compounded annually) after-tax return on investments. What serial payment should Pat invest at the end of the first year to attain his goal?
A) $94,307.53
B) $92,458.37
C) $102,081.51
D) $104,123.14
A) $94,307.53
The answer is $94,307.53.
END Mode
1, DOWNSHIFT, P/YR
C ALL
500,000, FV,
5, DOWNSHIFT, N (5 periods show on display)
{[(1.06 ÷ 1.02) – 1] × 100} = 3.9216, I/YR
Solve for PMT = ‒92,458.3658 × 1.02 = ‒94,307.5331, or $94,307.53 (change sign)
77
What would the inflation-adjusted interest rate be with a 6% rate of return and a 2.5% inflation rate (rounded to two decimal places)?
A) 0.97%
B) 1.03%
C) 3.41%
D) 2.40%
C) 3.41%
The answer is 3.41%.
[(1.06 ÷ 1.025) ‒ 1] × 100 = 3.4146 (3.41, rounded)
78
Calculate the number of years it will take $100,000 to grow to $5,000,000 assuming an annual rate of return of 7%, compounded monthly (rounded to two decimal places).
A) 56.05
B) 693.84
C) 57.82
D) 672.59
A) 56.05
The answer is 56.05.
END Mode
12, DOWNSHIFT, P/YR
C ALL
100,000, +/‒, PV
7, I/YR
5,000,000, FV
Solve for N = 672.5866 months = 56.0489 years (56.05, rounded)
79
Mike borrowed $120,000 from his father, a banker, to purchase a house. Mike repaid $300,000 to his father at the end of 20 years. What was the average annual compound rate of interest on Mike's loan from his father?
A) 3.76
B) 4.69
C) 4.48
D) 4.89
B) 4.69
The answer is 4.69.
END Mode
1, DOWNSHIFT, P/YR
C ALL
20, DOWNSHIFT, N (20 periods shows on display)
120,000, PV
300,000, +/‒, FV
Solve for I/YR = 4.6880 (4.69 rounded)
80
Fred purchased 1,000 shares of XYZ stock three years ago for $20,000. The stock paid him a dividend of $400 at the end of the first year, $500 at the end of the second year, and $550 at the end of the third year. At the end of the third year, Fred sold all the shares for $23,000. What was Fred's internal rate of return (IRR) on the stock?
A) 15.00%
B) 7.06%
C) 5.31%
D) 7.00%
B) 7.06%
The answer is 7.06%.
END Mode
1, DOWNSHIFT, P/YR
C ALL
20,000, +/−,CFj
400, CFj
500, CFj;
23,550, CFj, DOWNSHIFT, IRR/YR = 7.0625, or 7.06%.
81
Rodney wants to start saving for a lump-sum amount of $200,000 (in today's dollars) that is needed in five years. He assumes an inflation rate of 3% and a before-tax rate of return of 7% on any investments that are set aside to meet this goal. How much must Rodney deposit at the end of each of the five years using the level payment approach?
A) $41,526.91
B) $40,317.39
C) $28,476.37
D) $37,679.68
B) $40,317.39
The answer is $40,317.39. The required annual savings deposit is $40,317.39 with keystrokes on the HP 10bII/HP 10bII+ as follows:
Step 1:
END Mode
1, DOWNSHIFT, P/YR
C ALL
200,000, +/−, PV
3, I/YR
5, DOWNSHIFT, N (5 periods show on display)
Solve for FV = 231,854.8149
Step 2:
C ALL
231,854.8149, FV
7, I/YR
5, N
Solve for PMT = –40,317.3948, or $40,317.39
82
A client invested $10,000 in an interest-bearing account earning an 11% annual rate of interest, compounded monthly. How much will the account be worth at the end of seven years, assuming all interest is reinvested at the 11% rate?
A) $20,763
B) $21,049
C) $21,522
D) $13,788
C) $21,522
The answer is $21,522.
END Mode
12, DOWNSHIFT, P/YR
C ALL
10,000, +/−, PV;
11, I/YR;
7, DOWNSHIFT, N (84 periods show on display)
Solve for FV = 21,522.0361 or $21,522.
83
Phan wants to withdraw $2,500 at the beginning of each year for the next five years. He wants to have $10,000 left at the end of the five years. Phan expects to earn 5% compounded annually on his investment. What lump sum should he deposit today?
A) $19,200
B) $10,824
C) $11,364
D) $18,659
A) $19,200
The answer is $19,200.
BEG Mode
1, DOWNSHIFT, P/YR
C ALL
2,500, PMT
5, I/YR
5, DOWNSHIFT, N (5 periods show on display)
10,000, FV
Solve for PV = ‒19,200.1379, or $19,200.
84
Billy purchased a certificate of deposit five years ago for $1,700. If the certificate of deposit is due today in the amount of $2,000, what is the average annual compound rate of return, assuming monthly compounding, that Billy realized on his investment?
A) 0.28%
B) 0.27%
C) 3.30%
D) 3.25%
D) 3.25%
The answer is 3.25.
END Mode
12, DOWNSHIFT, P/YR
C ALL
5, DOWNSHIFT, N (60 periods show on display)
1,700, +/‒, PV
2,000, FV
Solve for I/YR = 0.2712 × 12 = 3.2548, 3.25% rounded
85
Dominic and Andrea would like to save $40,000 for a down payment toward the purchase of a new home. If they deposit $450 at the beginning of each month into an investment earning an annual rate of return of 9%, compounded monthly, approximately how long will it take for them to accumulate the down payment?
A) 5.75 years
B) 5.34 years
C) 6 years
D) 5.66 years
D) 5.66 years
The answer is 5.66 years.
BEG Mode
12, DOWNSHIFT, P/YR
C ALL
40,000, FV
9, I/YR
450, +/−, PMT
Solve for N = 67.9661 months ÷ 12 years = 5.6638, or 5.66 years.
86
Max acquires a $200,000 mortgage with a 30-year repayment term and an annual interest rate of 5%. What is the balance of Max's mortgage after 12 monthly payments?
A) $197,049
B) $193,333
C) $198,229
D) $190,067
A) $197,049
The remaining mortgage balance after 12 payments is $197,049.
END Mode
12, DOWNSHIFT, P/YR
C ALL
200,000, PV;
5, I/YR
30 , DOWNSHIFT, N (360 periods show on display)
Solve for PMT = –1,073.6432.
Without clearing the calculator:
1, INPUT, 12, DOWNSHIFT, AMORT (pressing the = key toggles you through amortization totals for months 1 through 300, see below)
Enter = –2,950.73 (total principal paid through 12 months)
Enter = –9,932.9884 (total interest paid through 12 months)
Enter = 197,049.27 (remaining mortgage balance at the end of 12 months).
87
Sarah borrowed $10,000 from her aunt to donate to charity. Sarah repaid $7,000 to her aunt at the end of three years. What was the average annual compound rate of interest on Sarah's loan from her aunt?
A) 10.20%
B) ‒11.21%
C) 12.62%
D) ‒12.22%
B) ‒11.21%
The answer is ‒11.21%.
END Mode
1, DOWNSHIFT, P/YR
C ALL
3, DOWNSHIFT, N (3 periods show on display)
10,000, PV
7,000, +/‒, FV
Solve for I/YR = ‒11.2096, (‒11.21% rounded)
The interest rate is negative because Sarah paid back less than what she borrowed.
88
Caleb secures a $350,000 mortgage with a 30-year repayment term and an annual interest rate of 6%. If he makes monthly payments, how much total interest will Caleb have paid on the mortgage at the end of 25 years?
A) $388,070.37
B) $108,542.33
C) $241,457.67
D) $375,960.34
A) $388,070.37
The answer is $388,070.37.
END Mode
12, DOWNSHIFT, P/YR
C ALL
350,000, PV
30, DOWNSHIFT, N (360 periods show on display)
6, I/YR
Solve for PMT = –2,098.4268
1, INPUT, 300, SHIFT, AMORT (pressing the = key toggles you through amortization totals for months 1 through 300, see below)
Enter = –241,457.6682 (total principal paid through 300 months)
Enter = –388,070.3718 (total interest paid through 300 months)
Enter = 108,542.3318 (remaining principal balance through 300 months).
89
A client wants to save $125,000 to achieve a future goal. He has $26,000 to invest currently and can invest $10,000 at the end of each year toward his goal. If the investment vehicle selected earns 10% annually, how many years will it take to achieve his goal?
A) 4.93
B) 5.74
C) 6.08
D) 6.18
C) 6.08
The answer is 6.08.
END Mode
1, DOWNSHIFT, P/YR
C ALL
10, I/YR
26,000, +/‒, PV
10,000, +/‒, PMT
125,000, FV
Solve for N = 6.0835 (6.08 years, rounded)
90
Nicole wants to withdraw $4,000 at the beginning of each year for the next seven years. She expects to achieve an after-tax annual growth rate of 10.5% on her investment. What lump sum should Nicole deposit today?
A) $18,667
B) $19,157
C) $20,627
D) $21,169
D) $21,169
The answer is $21,169.
BEG Mode
1, DOWNSHIFT, P/YR
C ALL
4,000, PMT
10.5, I/YR
7, DOWNSHIFT, N (7 periods show on display)
Solve for PV = −21,168.7176, or $21,169.
91
Les secures a $200,000 mortgage with a 30-year repayment term and an annual interest rate of 5.5%. How much principal will Les have paid on his original mortgage balance after the first 12 months?
A) $13,626.94
B) $10,932.76
C) $2,694.18
D) $2,825.99
C) $2,694.18
The answer is $2,694.18.
END Mode
12, DOWNSHIFT, P/YR
C ALL
200,000, PV
30, DOWNSHIFT, N
5.5, I/YR
Solve for PMT = –1,135.5780
Enter 1, INPUT, 12, SHIFT, AMORT (pressing the = key toggles you through amortization totals for months 1 through 12)
Enter = –2,694.1789 (total principal paid through 12 months)
Enter = –10,932.7571 (total interest paid through 12 months)
Enter = 197,305.8211 (remaining principal balance through 12 months).
92
At the beginning of each year for the past 20 years, Waleed has put $5,000 into an account earning 4% annually. How much is the account worth today?
A) $154,846
B) $148,890
C) $70,670
D) $67,952
A) $154,846
The answer is $154,846.
BEG Mode
1, DOWNSHIFT, P/YR
C ALL
5,000, +/−, PMT
4, I/YR
20, DOWNSHIFT, N (20 periods show on display)
Solve for FV = 154,846.0086, or $154,846.
93
John wants to start his own business in six years and will need $200,000. He assumes inflation will average 4% and that he can earn a 9% compound annual after-tax rate of return on his investments. What serial payment should John invest at the end of the first year to attain his goal?
A) $28,190.78
B) $29,546.11
C) $30,727.95
D) $29,318.41
C) $30,727.95
The answer is $30,727.95.
END Mode
1, DOWNSHIFT, P/YR
C ALL
200,000, FV
[(1.09 ÷ 1.04) − 1] × 100 = 4.8077, I/YR
6, DOWNSHIFT, N (6 periods show on display)
Solve for PMT = -29,546.1090 × 1.04 = -30,727.9533, or $30,727.95 (change sign)
94
If the net present value (NPV) of a series of discounted cash flows is equal to zero, one could interpret that
I. the discounted cash flows equal the investment outlay.
II. the rate of return is lower than the cost of capital.
III. the return on investment is lower than the internal rate of return.
IV. the internal rate of return was the discount rate.
A) II only
B) I and IV
C) II and III
D) I only
B) I and IV
The net present value (NPV) of a series of discounted cash flows equal to zero means the discounted cash flows are equal to the investment outlay. This also means that the internal rate of return is the discount rate.
95
Gilbert purchased several gold coins for $30,000. Today, he sold the coins for $55,045.91. Gilbert estimated the average annual rate of return, compounded monthly, on the coins was 9%. Approximately how many years did Gilbert own the coins (rounded to the nearest 0.00)?
A) 7.04
B) 84.52
C) 6.77
D) 81.23
C) 6.77
The answer is 6.77.
END Mode
12, DOWNSHIFT, P/YR
C ALL
9, I/YR
30,000, +/‒, PV
55,045.91, FV
Solve for N = 81.2325 months ÷ 12 years = 6.7694 years (6.77, rounded)
96
Joe is considering purchasing a machine that will cost $10,000 for 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 internal rate of return (IRR) for Joe's anticipated purchase.
A) 5.82%
B) 28.00%
C) 6.18%
D) 5.49%
A) 5.82%
The answer is 5.82%.
END Mode
1, DOWNSHIFT, P/YR
C ALL
10,000, +/−, CFj
300, CFj
600, CFj
1,200, CFj
2,400, CFj
8,300, CFj
DOWNSHIFT, IRR/YR = 5.8229, or 5.82%
97
Bill purchased $60,000 worth of silver coins eight years ago. The coins have appreciated at a rate of 7.5% compounded annually over that period. How much are the coins worth today?
A) $99,719.03
B) $102,829.46
C) $99,542.95
D) $107,008.67
D) $107,008.67
The answer is $107,008.67.
END Mode
1, DOWNSHIFT, P/YR
C ALL
60,000, +/‒. PV
7.5, I/YR
8, DOWNSHIFT, N (8 periods show on display)
FV = 107,008.6895, or $107,008.67
98
A client would like to accumulate $300,000 for retirement, which will begin in 10 years. She can invest $10,000 at the end of each year toward this goal in an account earning 8% annually. What initial lump-sum deposit, in addition to the payment stream, is required for her to be able to meet this goal?
A) $62,050.09
B) $71,857.23
C) $85,730.74
D) $66,489.17
B) $71,857.23
The answer is $71,857.23.
END Mode
1, DOWNSHIFT, P/YR
C ALL
10, DOWNSHIFT, N (10 periods show on display)
8, I/YR
300,000, FV
10,000, +/‒, PMT
Solve for PV = $71,857.23
The initial deposit required to meet the client's goal is $71,857.23.
99
Carmen has refinanced her mortgage of $200,000 for 15 years with an annual interest rate of 5%. How much is her monthly principal and interest payment?
A) $1,581.59
B) $1,575.02
C) $1,529.24
D) $1,605.70
A) $1,581.59
The answer is $1,581.59.
END Mode
12, DOWNSHIFT, P/YR
C ALL
200,000, PV
5, I/YR
15, DOWNSHIFT, N (180 periods show on display)
Solve for PMT = –1,581.5873, or $1,581.59.
100
Sarah wants to start her own business in six years. She needs to have accumulated $200,000 (in today's dollars) in six years to sufficiently finance her business. She assumes inflation will average 4% and that she can earn a 9% compound annual after-tax rate of return on investments. What will be Sarah's serial payment at the end of the second year?
A) $30,727.95
B) $30,491.00
C) $31,957.07
D) $28,190.78
C) $31,957.07
The answer is $31,957.07.
END Mode
1, DOWNSHIFT, P/YR
C ALL
200,000, FV
[(1.09 ÷ 1.04) − 1] × 100 = 4.8077, I/YR
6, DOWNSHIFT, N (6 periods show on display)
PMT = ‒29,546.1032 × 1.04 = -30,727.9474, or $30,727.95 (change sign)
30,727.95 × 1.04 = $31,957.07
101
Aurelia wants to purchase a home six years from today for $150,000. To attain this goal, how much should she invest at the end of each six-month period if she expects to earn a 12% annual rate of return, compounded semiannually, on her investments?
A) $8,891.55
B) $8,388.26
C) $18,483.86
D) $16,503.44
A) $8,891.55
The answer is $8,891.55.
END Mode
2, DOWNSHIFT, P/YR
C ALL
150,000, FV
12, I/YR
6, DOWNSHIFT, N (12 periods show on display)
Solve for PMT = ‒8,891.5544, or $8,891.55
102
An investor makes an initial deposit of $20,000 into a mutual fund. Each subsequent year he deposits an additional $2,500 into the fund. What will be the value of the account in eight years if the fund earns 9% annually?
A) $12,280.07
B) $67,422.44
C) $69,903.84
D) $69,798.66
B) $67,422.44
The answer is $67,422.44.
END Mode
1, DOWNSHIFT, P/YR
C ALL
8, DOWNSHIFT, N (8 periods show on display)
9, I/YR
20,000, +/‒, PV
2,500, +/‒, PMT
Solve for FV = 67,422.4373, or $67,422.44
The account value after eight years would be $67,422.44.
103
What is the number one reason that students will incorrectly answer a time value of money problem on the CFP® exam?
Not clearing the calculator properly after every problem.
104
? is the process of determining the present value of a future amount of money or cash flow by applying a discount rate. It is based on the principle that money available today is worth more than the same amount in the future due to its potential earning capacity, often referred to as the time value of money (TVM).
Discounting.
105
Loan amortizations (e.g., mortgages, auto loans) are calculated using which mode on the calculator?
END mode.
The interest on the principal balance is accruing from payment to payment on the balance of the debt.
106
Most of the calculations involving unequal cash flows will require solving for the compound return, also known as the ?, or for the PV of an asset.
internal rate of return (IRR)
107
If the NPV is ?, it means that the investment would earn a return more than the discount rate (required rate of return). If the NPV is ?, it means the investor would earn a return less than the discount rate.
positive; negative
107
NPV of investment = ? - ?
PV of cash flows - cost of investment
