Module 4

Question 1

Compounding

Answer 1

The process of interest being earned on increasing sums of principal and interest over time.

Question 2

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?

Answer 2

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

Question 3

Annuity

Answer 3

If the payments are equal and regular, the series of savings deposits or payments is called (in time value of money language) an annuity.

Question 4

Future Value of an Annuity

Answer 4

The accumulation of funds needed to meet a future financial goal.

Question 5

Annuity Due

Answer 5

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.

Question 6

Ordinary Annuity

Answer 6

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.

Question 7

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?

Answer 7

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

Question 8

With respect to calculator entry, whenever you are solving for the future value (FV) of an annuity, which key must be used?

Answer 8

The payment (PMT) key.

Question 9

As with the FV process, the PV of a single amount depends on the:

Answer 9

„ 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.

Question 10

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?

Answer 10

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.)

Question 11

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?

Answer 11

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

Question 12

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?

Answer 12

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

Question 13

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?

Answer 13

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%

Question 14

If you change P/YR to an amount other than 1 (annual), you should:

Answer 14

enter the number of years, followed by “DOWNSHIFT, xP/YR”.

Question 15

Rule of 72

Answer 15

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%.

Question 16

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?

Answer 16

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

Question 17

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?

Answer 17

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

Question 18

Fixed (equal) Payments

Answer 18

Unchanging payments over the entire period.

Question 19

Serial Payments

Answer 19

Payments increase each year by the amount of inflation (to maintain a constant or real dollar amount).

Question 20

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?

Answer 20

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.)

Question 21

Loan amortizations (e.g., mortgages, auto loans) are calculated using what mode?

Answer 21

END mode because the interest on the principal balance is accruing from payment to payment on the balance of the debt.

Question 22

Amortization

Answer 22

Refers to the repayment of loan principal over time.

Question 23

Amortization Schedule

Answer 23

Refers to how much principal and how much interest is being repaid with each payment.

Question 24

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?

Answer 24

„ 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

Question 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?

Answer 25

„ 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)

Question 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?

Answer 26

„ 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%

Question 27

What is the equation for inflation-adjusted interest rates?

Answer 27

[(1 + rate of return) / (1 + rate of inflation)] -1] x 100

Question 28

What would the inflation-adjusted interest rate be with a 7% rate of return and a 3% inflation rate?

Answer 28

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)

Question 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?

Answer 29

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

Question 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?

Answer 30

„ 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.

Question 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?

Answer 31

„ 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

Question 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?

Answer 32

„ 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.

Question 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?

Answer 33

„ 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.

Question 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?

Answer 34

„ 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.

Question 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?

Answer 35

„ 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.

Question 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?

Answer 36

„ 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.

Question 37

Internal Rate of Return (IRR)

Answer 37

Rate of growth that an investment is expected to generate.

Question 38

If NPV is being calculated, CF0 is input as:

Answer 38

A zero.

Question 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?

Answer 39

„ 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%.

Question 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?

Answer 40

„ 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.

Question 41

PV of Cash Flows - Cost of Investment = ?

Answer 41

NPV of investment.

Question 42

If the NPV is positive, it means that the investment would:

Answer 42

Earn a return more than the discount rate (required rate of return).

Question 43

If the NPV is negative, it means the investment would:

Answer 43

Earn a return less than the discount rate.

Question 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?

Answer 44

„ 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%

Question 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%?

Answer 45

„ 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%.

Question 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.

Answer 46

$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

Question 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.

Answer 47

$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

Question 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.

Answer 48

$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

Question 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.

Answer 49

$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

Question 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.

Answer 50

$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

Question 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?

Answer 51

$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

Question 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.

Answer 52

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%

Question 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.

Answer 53

$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

Question 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.

Answer 54

$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

Question 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).

Answer 55

$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

Question 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

Answer 56

• 4.39%
• 6.73%
• 2.45%

Question 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?

Answer 57

$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

Question 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?

Answer 58

$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

Question 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%.

Answer 59

$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

Question 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%

Answer 60

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

Question 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.

Answer 61

$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

Question 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?

Answer 62

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%

Question 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?

Answer 63

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.

Question 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)?

Answer 64

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%

Question 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?

Answer 65

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%

Question 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

Answer 66

$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

Question 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

Answer 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

Question 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

Answer 68

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.

Question 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

Answer 69

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.

Question 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

Answer 70

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

Question 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

Answer 71

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.

Question 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

Answer 72

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.

Question 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

Answer 73

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)

Question 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.

Answer 74

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.

Question 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

Answer 75

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

Question 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

Answer 76

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)

Question 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%

Answer 77

C) 3.41%

The answer is 3.41%.

[(1.06 ÷ 1.025) ‒ 1] × 100 = 3.4146 (3.41, rounded)

Question 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

Answer 78

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)

Question 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

Answer 79

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)

Question 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%

Answer 80

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%.

Question 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

Answer 81

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

Question 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

Answer 82

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.

Question 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

Answer 83

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.

Question 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%

Answer 84

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

Question 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

Answer 85

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.

Question 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

Answer 86

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).

Question 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%

Answer 87

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.

Question 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

Answer 88

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).

Question 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

Answer 89

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)

Question 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

Answer 90

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.

Question 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

Answer 91

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).

Question 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

Answer 92

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.

Question 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

Answer 93

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)

Question 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

Answer 94

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.

Question 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

Answer 95

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)

Question 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%

Answer 96

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%

Question 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

Answer 97

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

Question 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

Answer 98

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.

Question 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

Answer 99

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.

Question 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

Answer 100

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

Question 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

Answer 101

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

Question 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

Answer 102

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.

Question 103

What is the number one reason that students will incorrectly answer a time value of money problem on the CFP® exam?

Answer 103

Not clearing the calculator properly after every problem.