Time Value of Money (TVM)

Question 1

Tracy purchased a car for $19,500. She is financing the purchase at an 11% annual interest rate, compounded monthly for 3 years. What is the payment that Tracy is required to make at the end of each month?

A. $606.71
B. $632.61
C. $638.40
D. $684.97

Answer 1

N = 3 x12
i = 11 ÷ 12
PV = 19,500
FV = 0
Solve for PMT (= $638.4049838)

Question 2

Jason received a check for $50,000 today. This was from an investment made 10 years ago. The investment earned 8% compounded quarterly. How much was his original investment?

A. $41,017
B. $22,645
C. $16,035
D. $23,160

Answer 2

N = 10 x 4 = 40
i = 8 ÷ 4 = 2
PV = 22,644.52
PMT = 0
FV = 50,000

Question 3

Lori wants to give her daughter $25,000 in 8 years to start her own business. How much should Lori invest today, at an annual interest rate of 8%, compounded annually, to have $25,000 in 8 years?

A. $12,802.95
B. $13,210.34
C. $13,347.70
D. $13,506.72

Answer 3

N = 8
i = 8
PMT = 0
FV = 25,000
Solve for PV (= 13,506.7211)

Question 4

Bob and his wife Sally recently opened an investment account with the intention of saving enough to purchase the house of their dreams. Their goal is to have $45,000 down in 5 years. Their account will guarantee them a return of 8% compounded annually. How much do they need to put into the account right now to reach their objective?

A. $46,778.96
B. $39,546.09
C. $51,214.75
D. $30,626.24

Answer 4

D. $30,626.24

N = 5
i = 8
PV = ?
PMT = 0
FV = 45,000

Question 5

Holly is considering purchasing a new car for $30,000. The dealer is offering two mutually exclusive options on the purchase:

Option #1: Receive a $4,000 rebate on the price of the car and finance the balance over 5 years at 4% interest, or

Option #2: Finance the vehicle for 7 years at 0% interest with no rebate.

Which of the following options should Holly select if her goal is to minimize the total amount she pays for the car?

A. Option 1 is better.
B. Option 2 is better.
C. Both options cost the same.
D. There is not enough information to answer the question.

Answer 5

Option #1:
N = 5 x 12
i = 4 ÷12 = 0.333
PV = 30,000 - 4,000 = 26,000
PMT = ?
FV = 0
478.83 x 60 = 28,729.77
Total paid = $28,729.77

Option #2:
Cost is $30,000
Total paid = $30,000

Question 6

Anthony has been investing $1,000 at the end of each year for the past 15 years. How much has accumulated assuming he has earned 10.5% compounded annually on his investment?

A. $20,303.72
B. $23,349.28
C. $33,060.04
D. $36,531.34

Answer 6

C. $33,060.04
N = 15
i = 10.5
PV = 0
PMT = 1,000
FV = $33,060.04

Question 7

Colin is trying to decide whether he should make his IRA contribution at the beginning of the year or at the end of the year. He wants to save $5,000 per year for 25 years in his IRA that can earn 7% per year. What would be the difference in his account value if he made the payments at the beginning of each year rather than at the end?

A. $338,382
B. $22,137
C. $28,041
D. $316,245

Answer 7

B. $22,137
N = 25 N = 25
i = 7 i = 7
PV = 0 PV = 0
PMTAD = 5,000 PMTOA = 5,000
FV = ? FV = ?
338,382 316,245
338,382 - 316,245 = 22,137

Question 8

Hannah has decided to save for a vacation in 18 months. She will save the money into a short-term investment account returning 4% annually. How much will she have to put away at the beginning of each month if the vacation cost is $15,000? (Round to the nearest dollar.)

A. $815
B. $810
C. $807
D. $800

Answer 8

C. $807
BEGIN Mode
N = 18
i = 4 ÷ 12 = 0.3333
PV = 0
PMT = ?
FV = $15,000
PMTAD = $807.28

Question 9

Tony saved enough money to place $125,500 in an investment generating 9.25% compounded monthly. He wants to collect a monthly income of $1,350, at the beginning of each month, for as long as the money lasts. How many months will Tony have this income coming to him?

A. 165
B. 145
C. 192
D. 162

Answer 9

D. 162
BEGIN Mode
N = ?
i = 9.25 ÷ 12 = 0.7708
PV = -$125,500
PMT = $1,350
FV = 0

N = 161.7 (≈162)

Question 10

Your client invested $10,000 in an interest bearing promissory note earning an 11% annual rate of interest, compounded monthly. How much will the note be worth at the end of 7 years, assuming that all interest is reinvested at the 11% rate?

A. $13, 788.43.
B. $20,762.60.
C. $21,048.52.
D. $21,522.04.

Answer 10

D. $21,522.04
N = 7 x 12
i = 11 ÷ 12
PV = 10,0000
PMT = 0
Solve for FV (= 21,522.03612)

Question 11

Judy recently purchased her first home for $200,000. She made a down payment of $20,000, and financed the balance over 15 years, at 4.25% interest. If Judy’s first payment is due on October 1 of this year, approximately how much interest will she pay in this year?

A. $1,262.90
B. $2,989.67
C. $3,288.63
D. $5,885.09

Answer 11

A. $1,262.90
BEGIN MODE
N = 15 x 12
i = 4.25 ÷ 12
PV = 180,000
FV = 0
Solve for PMT = (1,349.32)

Enter the AMORT
P1 = 1
P2 = 3
Arrow down to INT

Question 12

Cindy invests $20,000 in a limited partnership today. At the end of each years 1 through 5, she will receive the after-tax cash flows shown below. The partnership will be liquidated at the end of the fifth year. Cindy is in the 35% federal income bracket.

Years Cash Flows
0 - $20,000
1 $0
2 $4,000
3 $6,000
4 $8,000
5 $10,000

The after-tax IRR on this investment is:

A. 6.01.
B. 7.26.
C. 8.15.
D. 9.24.

Answer 12

D. 9.24
CF0 = -$20,000
CF1 = $0
CF2 = $4,000
CF3 = $6,000
CF4 = $8,000
CF5 = $10,000
IRR = 9.24

Note: The question provides after-tax cash flows.

Question 13

Billy owns one share of Disney stock. He purchased the share 3 years ago for $15. Disney stock is currently trading for $25 per share. The stock has paid the following dividends over the past three years: year 1, $1.00; year 2, $2.00; year 3, $3.00.

What is the compounded rate of return (IRR) that Billy has earned on his investment?

A. 9.1%
B. 19.1%
C. 29.1%
D. 39.1%

Answer 13

C. 29.1%
CFo = (15)
CFj =1
CFj = 2
CFj = 25 +3
Solve for IRR (29.0622192)

Question 14

Jill would like to plan for her son’s college education. She would like for her son, who was born today, to attend college for 5 years, beginning at age 18. Tuition is currently $12,000 per year and tuition inflation is 6%. Jill can earn an after-tax rate of return of 8%. How much must Jill save at the end of each year, if she wants to make the last payment at the beginning of her son’s first year of college?

A. $3,145.81
B. $3,745.31
C. $4,080.32
D. $4,406.75

Answer 14

D. $4,406.75
STEP #1 – Solve for FV
N = 18
i: 6%
PV: -$12,000
PMT: 0
FV: ?

FV = $34,252.07

STEP #2 – Solve for PV with IARR (use Google Sheet)
N = 5
i/IARR: 1.89%
PV: ?
PMT: -$34,252.07 (using FV from Step 1)
FV: $0

PV: $181,201.68

STEP #3 – Solve for PMT (*using PV from Step #2)
N = 18
i: 8%
PV: $0
PMT: ?
FV: -$165,033.75

PMT: $4,406.75

Question 15

Ted has been dollar cost averaging in a mutual fund by investing $1,500 at the beginning of every quarter for the past 5 years. He has been earning an average annual compound return of 9% compounded quarterly on this investment. How much is the fund worth today?

A. $37,367.28
B. $38,208.04
C. $39,876.90
D. $41,342.56

Answer 15

B. $38,208.04
BEGIN MODE
N = 5 x 4
i = 9 ÷ 4
PV = 0
PMT = 1,500
FV = ?

Question 16

Which of the following is/are correct?

1. The IRR is the discount rate which equates the present value of an investment’s expected costs to the present value of the expected cash inflows.
2. If the cost of capital for this investment is 9% and the IRR is 9.24, the investment should be rejected.

A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Answer 16

Only statement #1 is true. When IRR is higher than cost of capital, the project would be acceptable.

Question 17

Brandon buys a piece of equipment for $15,000. He pays $5,000 for upgrades in year 1 and the equipment generates $2,000 in cash flow for year 1. In year 2 the equipment generates $8,000, year 3 it generates $4,000, but Brandon sells it for $6,000 but also pays a $500 commission. What is his IRR?

A. -1.18%
B. +1.18%
C. -0.8%
D. +0.8%

Answer 17

CF0 = -15,000
CF1 = -3,000
CF2 = 8,000
CF3 = 4,000 + 6,000 - 500 = $9,500

IRR = -1.18%

Question 18

The Keller’s discovered that they could reduce their mortgage interest rate from 10% to 4%. The value of homes in their neighborhood has been increasing at the rate of 5% annually. If the Keller’s were to refinance their house with $3,000 in closing costs added to their current mortgage balance ($277,000) over a period of time which coincides with their chosen retirement age in 20 years, what would be their new monthly payment including principal and interest?

A. $1,672.99.
B. $1,678.56
C. $1,691.11
D. $1,696.74

Answer 18

D. $1,696.74
USE LOAN GOOGLE SHEET
N = 240
i = 4 ÷ 12
PV = $280,000
PMT = ?
FV = $0

Question 19

All of the following statements regarding NPV are true EXCEPT:

A. A positive NPV indicates the present value of the cash flows exceeds the initial investment.
B. A negative NPV indicates the present value of the cash flows is less than the initial investment.
C. An NPV equal to zero indicates the present value of the cash flows is equal to the initial investment.
D. The internal rate of return is the discount rate that causes the initial investment to exceed the present value of the cash flows.

Answer 19

D. The internal rate of return is the discount rate that causes the initial investment to exceed the present value of the cash flows.

Explanation:
IRR sets the initial investment equal to the present value of the cash flows.

Question 20

Brandon buys a piece of equipment for $15,000. He pays $5,000 for upgrades in year 1 and the equipment generates $2,000 in cash flow for year 1. In year 2 the equipment generates $8,000, year 3 it generates $4,000, but Brandon sells it for $6,000 but also pays a $500 commission. Assume a required rate of return of 8%. What is the NPV?

A. <3,378>
B. 3,378.
C. <2,178>
D. 2,178

Answer 20

A. <3,378>

CF0 =
CF1 = 2,000
CF2 = 8,000
CF3 = 4,000 + 6,000 - 500 = $9,500

i = 8
NPV = ?

Question 21

Joey, injured in an automobile accident, won a judgment that provides him $1,500 at the end of each 6 month period over the next 6 years. If the escrow account that holds Joey’s settlement award earns an annual average rate of 12% compounded semiannually, how much was the defendant initially required to pay Joey to compensate him for his injuries?

A. Not enough information to calculate
B. $8,324.01
C. $11,023.23
D. $12,575.77

Answer 21

D. $12,575.77
N = 6*2 = 12
I/Y: 12%/2 = 6.00 %
PV = ?
PMT = $1,500.00
FV = $0

Question 22

Tim expects to receive $75,000 in 3 years. His opportunity cost is 16% compounded quarterly. What is this sum worth to Tim today?

A. 38,691.33
B. 46,844.78
C. 22,195.29
D. 42,699.43

Answer 22

B. 46,844.78
N = 4*3 = 12
i = 16.00% ÷ 4 = 4%
PV = ?
PMT = $0
FV= $75,000.00

Question 23

Marge has been dollar cost averaging in a mutual fund by investing 1,500 at the end of every quarter for the past 4 years. She has been earning an average annual compound return of 16% compounded quarterly on this investment. How much is the fund worth today?

A. $57,345.88
B. $29,773.22
C. $45,492.69
D. $32,736.80

Answer 23

D. $32,736.80
N = 4*4 = 16
i = 16.00% ÷ 4 = 4%
PV = $0
PMT = $1500
FV= ?

Question 24

Jason purchased $60,000 worth of silver coins 8 years ago. The coins have appreciated 8% compounded annually over the last 8 years. How much are the coins worth today?
A. $90,002.81
B. $111,055.81
C. $133,657.89
D. $98,400.00

Answer 24

B. $111,055.81
N = 8
i = 8.00%
PV = $60,000
PMT = $0
FV = ?

Question 25

Doris purchased a zero coupon bond 5 years ago for $675.68. If the bond matures today and the face value is $1,000, what is the average annual compound rate of return (calculated semiannually) that she realized on her investment?

A. 3.22%
B. 9.36%
C. 0.00%
D. 7.99%

Answer 25

N = 5*2 = 10
i = ?
PV = -$675.68
PMT = $0
FV = $1,000.00

i = 3.99% * 2 = 7.99%

Question 26

Brandon wants to accumulate $57,000 in 8 years to purchase a boat. He expects an annual rate of return of 10% compounded annually. How much does Brandon need to invest today to meet his goal?

A. $26,590.92
B. $57,000.00
C. $97,345.91
D. $22,599.23

Answer 26

A. $26,590.92
N =
i =
PV =
PMT =
FV =

Question 27

Andy borrowed $800 from his father to purchase a mountain bike. Andy paid back $1,175.20 to his father at the end of 5 years. What was the average annual compound rate of interest on Andy’s loan from his father?

A. 18.00%
B. 3.00%
C. 8.00%
D. 11.00%

Answer 27

C. 8.00%
N =
i =
PV =
PMT =
FV =

Question 28

Homer has been investing $3,000 at the beginning of each year for the past 16 years. How much has accumulated assuming he has earned 8% compounded annually on his investment?

A. $58,954.61
B. $52,356.99
C. $98,250.68
D. $90,287.44

Answer 28

C. $98,250.68
BEGIN MODE
N = 16*2 = 32
i = 8.00% ÷ 2 = 4.00%
PV = $0
PMT = -$3,000
FV = ?

Question 29

Maggie plans to invest in a mutual fund using dollar cost averaging, which means she will buy a fixed dollar amount on a regular schedule, regardless of the share value. She will buy more shares when the value per share is down and fewer when value is up. She plans to invest a fixed amount at the end of every quarter and earn an average annual compound return of 16% compounded quarterly on this investment. How much will she need to invest at the end of each quarter to have $32,000 at the end of four years?

A. $3,287.66
B. $4,000.00
C. $1,234.55
D. $1,466.24

Answer 29

D. $1,466.24
N = 4*4 = 16
i = 16.00% ÷ 4 = 4.00%
PV = $0
PMT = ?
FV = $32,000

Question 30

You need a loan for $50,000 to start up your new business. The loan will be amortized with quarterly payments over 4 years at 16% interest. What is the quarterly payment that you will need to make.

A. $3,222.22
B. $4,291.00
C. $6,234.77
D. $22,000.00

Answer 30

B. $4,291.00
N = 4*4 = 16
i = 16.00% ÷ 4 = 4.00%
PV = $50,000
PMT = ?
FV = $0

Question 31

A client owns one share of Walmart. She purchased the share 3 years ago for $18. Walmart stock is currently trading for $23 per share. The stock has paid the following dividends over the past three years: year 1, $1.00; year 2, $2.00; year 3, $3.00.

What is the compounded rate of return (IRR) that she has earned on her investment?

A. 18.25%.
B. 19.1%.
C. 39.1%.
D. 29.1%.

Answer 31

CFo = -$18
CFj = $1
CFj = $2
CFj = $23 + $3
Solve for IRR

Question 32

Jeff recently purchased a house for $350,000. He made a down payment of $50,000 and financed the balance over 30 years at 8%. If Jeff ‘s first payment is due on March 1st of the current year, how much interest expense will Jeff pay in the current year?

A. $19,938.54.
B. $17,819.73
C. $2,524.64.
D. $16,288.63.

Answer 32

N =
i =
PV =
PMT =
FV =

Question 33

Ted has been dollar cost averaging in a mutual fund by investing $1,500 at the beginning of every month for the past 5 years. He has been earning an average annual compound return of 9% compounded monthly on this investment. How much is the fund worth today?

A. $37,367.28.
B. $115,764.22
C. $38,208.04.
D. $113,984.73

Answer 33

N =
i =
PV =
PMT =
FV =

Question 34

Jim buys a piece of equipment for $10,000. He pays $5,000 for upgrades in year 1 and the equipment generates $2,000 in cash flow for year 1. In year 2 the equipment generates $8,000, year 3 it generates $4,000, but Jim sells it for $6,000 but also pays a $500 commission. What is his IRR?

A. 9.5%
B. 13.75%
C. -1.18%
D. 15.06%

Answer 34

CF0 = -$10,000
CF1 = -$5000 + 2000 = -$3000
CF2 = $8,000
CF3 = $4,000 + $6,000 - $500 = $9,500

IRR = ?

Question 35

Jill would like to plan for her son’s college education. She would like for her son, who was born today, to attend college for 5 years, beginning at age 18. Tuition is currently $14,000 per year and tuition inflation is 6%. Jill can earn an after-tax rate of return of 8%. How much must Jill save at the end of each year, if she wants to make the last payment at the beginning of her son’s first year of college?

A. $3,145.81
B. $5,141.20
C. $4,406.75
D. $3,745.31

Answer 35

STEP #1 – Solve for FV
N = 18
i: 6%
PV: -$14,000
PMT: 0
FV: ?

FV = $39,960.07

STEP #2 – Solve for PV with IARR (use Google Sheet)
N = 5
i/IARR: 1.89%
PV: ?
PMT: -$39,960.07 (using FV from Step 1)
FV: $0

PV: $192,539.38

STEP #3 – Solve for PMT (*using PV from Step #2)
N = 18
i: 8%
PV: $0
PMT: ?
FV: -$192,539.38

PMT: $5,141.20

Question 36

Samantha recently purchased her first home for $220,000. She made a down payment of $20,000, and financed the balance over 15 years, at 6% interest. If Samantha’s first payment is due on September 30 of this year, approximately how much interest will she pay in this year?

A. $2,073.47
B. $3,288.63
C. $5,885.09
D. $3,979.29

Answer 36

N = 15*12
i = 6% ÷ 12
PV = $200,000
PMT = ?
FV = $0

AMORT
P1 = 1
P2 = 4
Down Arrow until INT = -$3,979.30

Question 37

The Keller’s discovered that they could reduce their mortgage interest rate from 10% to 6%. The value of homes in their neighborhood has been increasing at the rate of 5% annually. If the Keller’s were to refinance their house with $3,000 in closing costs added to their current mortgage balance ($277,000) over a period of time which coincides with their chosen retirement age in 20 years, what would be their new monthly payment including principal and interest?

A. $2,034.11
B. $1,696.74
C. $2,006.01
D. $1,678.56

Answer 37

N = 20*12
i = 6% ÷ 12
PV = $280,000
PMT = ?
FV = $0

Question 38

Calculate the IRR of a machine that is purchased for $5,000, sold at the end of year 5 for $2,500, and produces the following cash flows:

Year 1: $700
Year 2: $800
Year 3: $900
Year 4:$1,000

A. 6.5%
B. 7.3%
C. 5.3%
D. 4.7%

Answer 38

CF0 = 5,000
CF1 = $700
CF2 = $800
CF3 = $900
CF4 = $1,000
CF5 = $2,500
IRR = 4.71%

Question 38

Cindy invests $18,000 in a limited partnership today. At the end of each years 1 through 5, she will receive the after-tax cash flows shown below. The partnership will be liquidated at the end of the fifth year. Cindy is in the 35% federal income bracket.

Years Cash Flows
0 - $18,000
1 $0
2 $4,000
3 $6,000
4 $8,000
5 $10,000

The after-tax IRR on this investment is:
A. 17.26%
B. 8.15%
C. 9.24%
D. 12.36%

Answer 38

CF0 = -$18,000
CF1 = $0
CF2 = $4,000
CF3 = $6,000
CF4 = $8,000
CF5 = $10,000
IRR = 12.36
Note: The question provides after-tax cash flows.

Question 39

As a financial advisor, what will you tell your client, Bill, he should be willing to pay for an investment property, given the following cash flows and the fact that he expects 10% on any investment he makes?

Today: ?
Year 1: $(10,000)
Year 2: $35,000
Year 3: $35,000
Year 4: $220,000

A. $191,231,57
B. $178,656,73
C. $189,910.29
D. $196,393.69

Answer 39

CF0 = 0
C01 = -$10,000
C02 = $35,000
C03 = $35,000
C04 = $220,000

i = 10%
NPV = $196,393.69