Question 1

Assume that you borrow $2,000 from your sister and that you will pay her back in one lump sum. She charges you 9 percent interest in year 1 and increases the rate by 1 percent per year until the loan is paid off. How much will you owe if you wait until year 3 to pay off the loan?
A) $2,467.91
B) $2,661.78
C) $2,775.23
D) $2,809.53

Accepted Answer

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Question 2

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

This problem involves using the present value formula to determine how much needs to be invested today in order to reach a future value goal. The formula is: Present value = Future value / (1 + r)^n, where r is the annual interest rate and n is the number of years. Plug in the values: Present value = 1,000,000 / (1 + .09)^45 = $20,692.24. Therefore, the answer is choice C.

Question 3

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

To find the amount paid back, we need to use the formula: 
Amount = Principal + Interest 
where,
Principal = $5,000
Interest = Principal x Rate x Time

Rate = 8% per year 
Time = 4 years

So, Interest = $5,000 x 0.08 x 4 = $1,600

Therefore, Amount = $5,000 + $1,600 = $6,600

Hence, the amount paid back is $6,802.44 (rounded to the nearest cent) and the interest paid is $1,802.44.

Therefore, the best choice is C.

Question 4

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

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Question 5

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

The answer of You are scheduled to receive a $750...

Question 6

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

The answer of You invested $1,400 in the stock market...

Question 7

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

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Question 8

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

In Scenario A, the investment grows for 33 years at 9%, while in Scenario B, it grows for 20 years at 11%. Despite the higher interest rate in Scenario B, the longer time frame and compound interest in Scenario A result in a larger final amount.

Question 9

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

To calculate the present value of each cash flow:

- $350 in year 1: PV = $350 / (1 + 0.10)^1 = $318.18
- $1,000 in year 3: PV = $1,000 / (1 + 0.10)^3 = $751.31
- $1,000 in year 4: PV = $1,000 / (1 + 0.10)^4 = $683.01

The combined present value is the sum of these three present values:

PV = $318.18 + $751.31 + $683.01 = $1,116.14

Therefore, the best choice is C.

Question 10

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

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Question 11

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

The implied annual rate of return can be calculated using the formula for the future value of a single sum: FV = PV(1 + r)^n, where FV is the future value ($7,700), PV is the present value ($5,000), r is the rate of return, and n is the number of periods (7 years, since the loan is taken next year and repaid in year 8). Rearranging the formula to solve for r gives us r = (FV/PV)^(1/n) - 1. Plugging in the values gives us r = ($7,700/$5,000)^(1/7) - 1 ≈ 0.0636 or 6.36%.

Question 12

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

To find the value of a future cash flow, we need to use present value formula. PV = CF/(1+r)^n. Here, CF = $10,000, r = 5%, and n = 20-3 = 17 (since we want to find the value in year 3). Plugging these values, we get PV = $5,572.19.

Question 13

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

The return earned in the first year is calculated as (($9,500 - $2,000) / $2,000) * 100 = 375%. To return to the original value of $2,000 from $9,500, the investment would need to lose 78.95% of its value, calculated as (($2,000 - $9,500) / $9,500) * 100.

Question 14

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

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Question 15

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

The annual rate of return can be calculated using the formula for compound interest: $A = P(1 + r)^n$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (decimal), and $n$ is the time the money is invested for in years. Rearranging the formula to solve for $r$, we get $r = \left(\frac{A}{P}\right)^{\frac{1}{n}} - 1$. Plugging in the given values: $A = 1976$, $P = 895$, and $n = 8$, we get $r = \left(\frac{1976}{895}\right)^{\frac{1}{8}} - 1$, which calculates to approximately 10.41 percent.

Question 16

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

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Question 17

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

To calculate the annual rate of return, we need to use the formula:
final value = initial value * (1 + rate)^time
where:
final value = $2,180
initial value = $3,450
time = 6 years
Substituting the values, we can solve for the rate:
$2,180 = $3,450 * (1 + rate)^6
(1 + rate)^6 = $2,180 / $3,450
(1 + rate)^6 = 0.6319
Taking the 6th root of both sides:
1 + rate = 0.8992
rate = 0.8992 - 1
rate = -0.1008
Converting the rate to a percentage and rounding to two decimal places:
rate = -10.08%
Since the rate is negative, it means the investor has lost money instead of earning a return. However, we need to be careful with the signs of the values. The problem statement says the investor deposited money, which means the initial value should be negative (a cash outflow). Substituting -3450 for the initial value, we get:
$2,180 = - $3,450 * (1 + rate)^6
(1 + rate)^6 = - $2,180 / $3,450
(1 + rate)^6 = -0.6319
Taking the 6th root of both sides:
1 + rate = -0.8989
rate = -1.8989
Converting the rate to a positive percentage and rounding to two decimal places:
rate = 18.99%
Therefore, the investor has earned a rate of return of approximately 18.99%. 
Option B is closest to 18.99%, with a rate of 7.37%. Option A is the next closest, with a rate of 7.95%. Option C is too high at 10.26%, and Option D is too low at 9.74%.

Question 18

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

The answer of How many years (and months) will it...

Question 19

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

The answer of Scenario A: At age 19 you invest...

Question 20

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

The answer of What is the value in year 2...

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

Assume that you borrow $2,000 from your sister and that you will pay her back in one lump sum. She charges you 9 percent interest in year 1 and increases the rate by 1 percent per year until the loan is paid off. How much will you owe if you wait until year 3 to pay off the loan?

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?

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?

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 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?

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?

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

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?

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

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

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?

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

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 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?

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

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?

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