Question 1

Assume you borrow $5,000 today and pay back the loan in one lump sum four years from today.You are charged 8 percent interest per year.What amount will you pay back and how much interest will you pay?
A) $6,399.56, $1,399.56
B) $6,508.21, $1,508.21
C) $6,802.44, $1,802.44
D) $7,902.11, $2,902.11

Accepted Answer

PV = 5000, N = 4, I = 8, FV = 6802.44 Int = 6802.44 − 5000 = 1802.44

Question 2

How many years (and months)will it take $1 million to grow to $3 million with an annual interest rate of 7.5 percent?
A) 15 years and 2.29 months
B) 17 years and 5.6 months
C) 18 years and 3.8 months
D) 19 years and 2.4 months

Accepted Answer

PV = 1, FV = 3, I = 7.5, => N = 15.1908 = 15 years and 2.29 months

Question 3

What is the value in year 2 of a $200 cash flow made in year 8 if interest rates are 3 percent?
A) $132.89
B) $147.23
C) $152.91
D) $167.50

Accepted Answer

FV = 200, N = 6, I = 3, => PV = 167.50

Question 4

You are scheduled to receive a $750 cash flow in one year,a $1,000 cash flow in two years,and pay a $300 payment in four years.If interest rates are 6 percent per year,what is the combined present value of these cash flows?
A) $1,359.92
B) $1,413.92
C) $1,592.63
D) $1,613.02

Accepted Answer

Step 1: FV = 750, N = 1, I = 6, => PV = 707.55
Step 2: FV = 1000, N = 2, I = 6, => PV = 890.00
Step 3: FV = −300, N = 4, I = 6, => PV = −237.63
Step 4: Sum of 3 PV = 1359.92

Question 5

An appliance store sells a TV for $1,200 and gives their customers a full three years to pay for the TV.If interest rates are 5 percent,what is the equivalent sales price of the TV when the customer takes the full 3 years to pay for it?
A) $991.72
B) $1,036.61
C) $1,104.14
D) $1,389.15

Accepted Answer

FV = 1200, N = 3, I = 5, => PV = 1036.61

Question 6

What annual rate of return is implied on a $5,000 loan taken next year when $7,700 must be repaid in year 8?
A) 6.36 percent
B) 7.12 percent
C) 8.54 percent
D) 11.62 percent

Accepted Answer

PV = 5000, N = 7, FV = 7700, => I = 6.36

Question 7

How many years (and months)will it take $4 million to grow to $7 million with an annual interest rate of 12 percent?
A) 4 years and 1.92 months
B) 4 years and 11.28 months
C) 5 years and 6.54 months
D) 5 years and 10.86 months

Accepted Answer

PV = 4, FV = 7, I = 12, => N = 4.94 = 4 years and 11.28 months

Question 8

What annual rate of return is earned on an $895 investment that grows to $1,976 in eight years?
A) 9.14 percent
B) 9.97 percent
C) 10.41 percent
D) 11.73 percent

Accepted Answer

PV = 895, n = 8, FV = 1976, => i = 10.41

Question 9

What is the value in year 3 of a $10,000 cash flow made in year 20 if interest rates are 5 percent?
A) $4,362.97
B) $4,491.27
C) $5,374.11
D) $5,572.19

Accepted Answer

FV = 10000, N = 17, I = 5, => PV = 4362.97

Question 10

Scenario A: At age 27,you invest $1,500 that earns 9 percent each year.Scenario B: At age 40,you invest $2,500 that earns 11 percent per year.Under which scenario do you accumulate more money by age 60?
A) Scenario A
B) Scenario B
C) Both scenarios have the same value by age 60.
D) Need more data to answer.

Accepted Answer

Scenario A: PV = 1500, N = 33, I = 9, => FV = 25773.04. Scenario B: PV = 2500, N = 20, I = 11, => FV = 20155.78.

Question 11

What annual rate of return is earned on a $13,000 investment made in year 2 when it grows to $17,000 by the end of year 7?
A) 10.64 percent
B) 4.28 percent
C) 8.04 percent
D) 5.51 percent

Accepted Answer

PV = 13000, FV = 17000, N = 5 => I = 5.51

Question 12

As the production manager of HPG,Inc.,you have received an offer from the supplier who provides the wires used in headsets.Due to poor planning,the supplier has an excess amount of wire and is willing to sell $750,000 worth for only $600,000.You already have one year's supply of wire on hand.This new wire would be used one year from today.What implied interest rate would your firm be earning if you purchased the wire?
A) −20 percent
B) 13.5 percent
C) 21 percent
D) 25 percent

Accepted Answer

N = 1, PV = 600000, FV = 750000, => I = 25.

Question 13

What would be more valuable,receiving $1,895 today or receiving $3,450 in six years if interest rates are 8 percent?
A) receiving $1,895 today
B) receiving $3,450 in six years
C) They are worth the same amount
D) Need more information to make a determination.

Accepted Answer

FV = 3450, N = 6, I = 8, => PV = 2174.09

Question 14

You are scheduled to pay a $350 cash flow in one year,and receive a $1,000 cash flow in years 3 and 4.If interest rates are 10 percent per year,what is the combined present value of these cash flows?
A) $991.38
B) $1,097.14
C) $1,116.14
D) $1,213.92

Accepted Answer

Step 1: FV = −350, N = 1, I = 10, => PV = −318.18.
Step 2: FV = 1000, N = 3, I = 10, => PV = 751.31.
Step 3: FV = 1000, N = 4, I = 10, => PV = 683.01.
Step 4: Sum of 3 PV = 1116.14.

Question 15

Ten years ago,Hailey invested $1,000 and locked in a 9 percent annual rate for 30 years (end 20 years from now).Aidan can make a 20-year investment today and lock in an 8 percent rate.How much money should he invest now in order to have the same amount of money in 20 years as Hailey?
A) $1,589.03
B) $2,846.56
C) $3,109.48
D) $2,109.73

Accepted Answer

Hailey: PV = 1000, N = 30, I = 9, => FV = 13267.67. Aidan: FV = 13267.67, N = 20, I = 8, => PV = 2846.56.

Question 16

You invested $1,400 in the stock market one year ago.Today the investment is valued at $1,100.What return did you earn? What return would you need to get back next year to break even overall?
A) −14.62 percent, 31.19 percent
B) −9.43 percent, 31.67 percent
C) −21.43 percent, 27.27 percent
D) −29.17 percent, 32.18 percent

Accepted Answer

Step 1: PV = 1400, FV = 1100, N = 1, => I = −21.43.
Step 2: PV = 1100, FV = 1400, N = 1, => I = 27.27.

Question 17

You invested $2,000 in the stock market one year ago.Today,the investment is valued at $9,500.What return did you earn? What return would you need to suffer next year for your investment to be valued at the original $2,000?
A) −78.95 percent, 0 percent
B) 375 percent, −78.95 percent
C) 250 percent, −51.8 percent
D) −78.95 percent, 100 percent

Accepted Answer

Step 1: PV = 2000, FV = 9500, N = 1, => I = 375.00.
Step 2: PV = 9500, FV = 2000, N = 1, => I = −78.95.

Question 18

A stock investor deposited $3,450 six years ago.Today the account is valued at $2,180.What annual rate of return has this investor earned?
A) 7.95 percent
B) 7.37 percent
C) 10.26 percent
D) 9.74 percent

Accepted Answer

PV = 3450, N = 6, FV = 2180, => I = −7.37

Question 19

You just won the lottery and after taxes you have $32,000.You want to have $1,000,000 by the time you are 65,which is 45 years from now.Assuming that you can earn 9 percent each year on your money,how much (in dollars)of the $32,000 must you invest today?
A) $17,891.62
B) $18,524.91
C) $20,692.24
D) $22,943.28

Accepted Answer

FV = 1000000, N = 45, I = 9, => PV = 20692.24

Question 20

Scenario A: At age 19 you invest $1,500 that earns 8 percent per year.Scenario B: At age 30 you invest $1,500 that earns 13 percent per year.Under which scenario would you have more money at age 55 and what is the dollar difference at age 55 between the two scenarios?
A) Scenario A, $1,085.49
B) Scenario A, $2,104.73
C) Scenario B, $4,179.36
D) Scenario B, $7,893.55

Accepted Answer

Scenario A: PV = 1500, N = 36, I = 8, => FV = 23952.26. Scenario B: PV = 1500, N = 25, I = 13, => FV = 31845.81 Difference = 31845.81 − 23952.26 = 7893.55.

Quiz 4: Time Value of Money 1: Analyzing Single Cash Flows

Assume you borrow $5,000 today and pay back the loan in one lump sum four years from today.You are charged 8 percent interest per year.What amount will you pay back and how much interest will you pay?

How many years (and months) will it take $1 million to grow to $3 million with an annual interest rate of 7.5 percent?

What is the value in year 2 of a $200 cash flow made in year 8 if interest rates are 3 percent?

You are scheduled to receive a $750 cash flow in one year,a $1,000 cash flow in two years,and pay a $300 payment in four years.If interest rates are 6 percent per year,what is the combined present value of these cash flows?

An appliance store sells a TV for $1,200 and gives their customers a full three years to pay for the TV.If interest rates are 5 percent,what is the equivalent sales price of the TV when the customer takes the full 3 years to pay for it?

What annual rate of return is implied on a $5,000 loan taken next year when $7,700 must be repaid in year 8?

How many years (and months) will it take $4 million to grow to $7 million with an annual interest rate of 12 percent?

What annual rate of return is earned on an $895 investment that grows to $1,976 in eight years?

What is the value in year 3 of a $10,000 cash flow made in year 20 if interest rates are 5 percent?

Scenario A: At age 27,you invest $1,500 that earns 9 percent each year.Scenario B: At age 40,you invest $2,500 that earns 11 percent per year.Under which scenario do you accumulate more money by age 60?

What annual rate of return is earned on a $13,000 investment made in year 2 when it grows to $17,000 by the end of year 7?

What would be more valuable,receiving $1,895 today or receiving $3,450 in six years if interest rates are 8 percent?

You are scheduled to pay a $350 cash flow in one year,and receive a $1,000 cash flow in years 3 and 4.If interest rates are 10 percent per year,what is the combined present value of these cash flows?

Ten years ago,Hailey invested $1,000 and locked in a 9 percent annual rate for 30 years (end 20 years from now) .Aidan can make a 20-year investment today and lock in an 8 percent rate.How much money should he invest now in order to have the same amount of money in 20 years as Hailey?

You invested $1,400 in the stock market one year ago.Today the investment is valued at $1,100.What return did you earn? What return would you need to get back next year to break even overall?

You invested $2,000 in the stock market one year ago.Today,the investment is valued at $9,500.What return did you earn? What return would you need to suffer next year for your investment to be valued at the original $2,000?

A stock investor deposited $3,450 six years ago.Today the account is valued at $2,180.What annual rate of return has this investor earned?

You just won the lottery and after taxes you have $32,000.You want to have $1,000,000 by the time you are 65,which is 45 years from now.Assuming that you can earn 9 percent each year on your money,how much (in dollars) of the $32,000 must you invest today?

Scenario A: At age 19 you invest $1,500 that earns 8 percent per year.Scenario B: At age 30 you invest $1,500 that earns 13 percent per year.Under which scenario would you have more money at age 55 and what is the dollar difference at age 55 between the two scenarios?