Question 1

A firm's net income last year was $2.65 million. Its net income grew 8 percent during the last "5" years. If that growth rate continues, how long will it take for the firm's net income to double?
A) 6.6 years
B) 7.1 years
C) 8.2 years
D) 9 years

Accepted Answer

The answer of A firm's net income last year was...

Question 2

Which of the following is the equivalent of $300 received today?
A) Seven hundred ninety-five dollars ninety-nine cents to be received 20 years in the future assuming a 5 percent annual interest rate.
B) Hundred dollars to be received two years from now and $200 three years from now.
C) Three hundred dollars compounded at 10 percent for one year.
D) All of these choices are correct.

Accepted Answer

The future value of $300 today at a 5% annual interest rate for 20 years is $300 * (1 + 0.05)^20 = $795.99, which matches option A.

Question 3

What is the value in year 10 of a $1,000 cash flow made in year 5 if interest rates are 9 percent in years 6 and 7, and increase to 13 percent in the remaining years?
A) $1,538.62
B) $1,691.47
C) $1,714.31
D) $1,799.42

Accepted Answer

To find the value in year 10 of a $1,000 cash flow made in year 5, we need to compound the cash flow forward in time using the given interest rates. For years 6 and 7, the interest rate is 9%, and for years 8 through 10, the interest rate increases to 13%.First, we compound the $1,000 for two years at 9%:Future Value after 2 years = $1,000 * (1 + 0.09)^2 = $1,000 * 1.1881 = $1,188.10Then, we compound this amount for the next 3 years at 13%:Future Value after 3 more years = $1,188.10 * (1 + 0.13)^3 = $1,188.10 * 1.4425 = $1,714.31Therefore, the value in year 10 of the $1,000 cash flow made in year 5 is $1,714.31.

Question 4

You invested $1,000 for five years in an account that earns 5 percent. However, today you learn that you are able to move the account into an investment that earns 10 percent. Which of the following statements is correct?
A) If you select the investment earning 10 percent, you will double your profit.
B) If you select the investment earning 10 percent, you will more than double your profit.
C) If you select the investment earning 10 percent, your profit will be less than double.
D) None of the statements is correct.

Accepted Answer

Moving the investment from a 5% return to a 10% return significantly increases the profit, more than doubling it due to the effect of compound interest over the remaining period.

Question 5

When your investment compounds, your money will grow in a(n) ________ fashion.
A) linear
B) exponential
C) static
D) implied

Accepted Answer

When your investment compounds, your money grows exponentially because you earn interest on both the initial principal and the accumulated interest from previous periods. This process results in an increasing rate of growth over time, unlike linear growth, where the increase is constant.

Question 6

Which of the following statements is incorrect with respect to time lines?
A) A helpful tool for organizing our analysis is the time line.
B) Cash flows we receive are called inflows and denoted with a positive number.
C) Cash flows we pay out are called outflows and designated with a negative number.
D) Interest rates are not included on our time lines.

Accepted Answer

Interest rates are often included on time lines to indicate the rate at which cash flows are discounted or compounded over time. Including interest rates helps in understanding the time value of money and in calculating present or future values of cash flows.

Question 7

A firm's net income last year was $1.5 million. Its net income grew 5 percent during the last "5" years. If that growth rate continues, how long will it take for the firm's net income to double?
A) 7.6 years
B) 10.47 years
C) 14.21 years
D) 14.55 years

Accepted Answer

To find how long it will take for the firm's net income to double, we use the Rule of 72, which is a simple way to estimate the number of years required to double the investment at a fixed annual rate of interest. Divide 72 by the annual growth rate: 72 / 5 = 14.4 years. The closest option is 14.21 years.

Question 8

A $1,000 investment has doubled to $2,000 in seven years. How much longer will it take for the investment to reach $5,000 if it continues to earn the same rate?
A) 6.16 years
B) 6.86 years
C) 7.15 years
D) 9.25 years

Accepted Answer

The answer of A $1,000 investment has doubled to $2,000...

Question 9

Which of the following investments would you prefer?
A) an investment earning 10 percent for 20 years
B) an investment earning 8.5 percent for 20 years
C) an investment earning 5 percent for 40 years
D) an investment earning 3 percent for 40 years

Accepted Answer

The answer of Which of the following investments would you...

Question 10

What is the value in year 6 of a $9,000 cash flow made in year 14 if interest rates are 7 percent in years "4 through 9" and increase to 10 percent after that?
A) $4,252.19
B) $4,417.46
C) $4,561.71
D) $45,798.53

Accepted Answer

To find the value in year 6 of a $9,000 cash flow made in year 14, we need to discount the cash flow back to year 6 using the given interest rates. From year 14 to year 9, the interest rate is 10%, and from year 9 to year 6, the interest rate is 7%. First, discount the cash flow from year 14 to year 9:$$PV_{9} = \frac{FV}{(1 + r)^n} = \frac{9000}{(1 + 0.10)^5} = \frac{9000}{(1.10)^5}$$$$PV_{9} = \frac{9000}{1.61051} = 5586.95$$Then, discount it from year 9 to year 6 using the 7% interest rate:$$PV_{6} = \frac{PV_{9}}{(1 + r)^n} = \frac{5586.95}{(1 + 0.07)^3} = \frac{5586.95}{(1.07)^3}$$$$PV_{6} = \frac{5586.95}{1.225043} = 4561.71$$Therefore, the value in year 6 of a $9,000 cash flow made in year 14 is $4,561.71.

Question 11

You want to retire in 40 years and you have $40,000 saved in your retirement account. You believe you will need $1,500,000 upon retirement. What rate will you need to earn on the account to achieve this goal?
A) 6.75 percent
B) 7.48 percent
C) 9.13 percent
D) 9.48 percent

Accepted Answer

The correct answer is D. 9.48 percent.The formula for calculating the future value of an investment is:FV = PV * (1 + r)^nwhere:FV is the future valuePV is the present valuer is the annual interest raten is the number of yearsIn this case, we have:PV = $40,000FV = $1,500,000n = 40Solving for r, we get:r = (FV / PV)^(1/n) - 1r = ($1,500,000 / $40,000)^(1/40) - 1r = 9.48%

Question 12

Which of the following would you prefer?
A) five hundred dollars to be received in 10 years when rates are 8 percent
B) three hundred dollars today
C) six hundred dollars to be received in 12 years when rates are 8 percent
D) seven hundred dollars to be received in 12 years when rates are 7 percent

Accepted Answer

The answer of Which of the following would you prefer?
A)...

Question 13

What is the value in year 4 of a $9,000 cash flow made in year 13 if interest rates are 7 percent in years "4 through 9" and increase to 11 percent after that?
A) $4,226.99
B) $4,472.06
C) $4,698.17
D) $4,716.52

Accepted Answer

The correct answer is A because the present value of the cash flow is $4,226.99. The present value is calculated by multiplying the cash flow by the present value factor. The present value factor is calculated by dividing 1 by (1 + r)^n, where r is the interest rate and n is the number of years. In this case, the interest rate is 7 percent for years 4 through 9 and 11 percent after that. The number of years is 13. So, the present value factor is 1 / (1 + 0.07)^9 * (1 + 0.11)^4 = 0.4703. The present value of the cash flow is $9,000 * 0.4703 = $4,226.99.

Question 14

Which of the following would you prefer?
A) four hundred dollars to be received in nine years when rates are 8 percent
B) two hundred ten dollars today
C) five hundred dollars to be received in 12 years when rates are 8 percent
D) five hundred dollars to be received in 12 years when rates are 9 percent

Accepted Answer

Option B, receiving $210 today, is preferable because the value of money today is worth more than the same amount in the future due to the potential earning capacity. This concept is known as the time value of money. Without calculating the present value of the other options, it's clear that having money now provides immediate utility and potential for investment, which could yield a higher return than the future values provided, especially when considering the impact of interest rates over time.

Question 15

A $400 investment has doubled to $800 in six years because of a 12.25 percent return. How much longer will it take for the investment to reach $1100 if it continues to earn 12.25 percent?
A) 2.56 years
B) 2.76 years
C) 3.46 years
D) 5 years

Accepted Answer

The investment grows according to the formula for compound interest: A = P(1 + r)^t, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), and t is the time the money is invested for in years. Since the investment has already grown to $800, we use this as our new principal amount (P) and want to find out how long (t) it will take to grow to $1100 at the same annual interest rate of 12.25% (or 0.1225 in decimal form). Rearranging the formula to solve for t gives us t = log(A/P) / log(1 + r). Plugging in the numbers gives us t = log(1100/800) / log(1.1225), which calculates to approximately 2.76 years.

Question 16

You want to retire in 25 years and you have just inherited $300,000. You believe you will need $1,450,000 upon retirement. What rate will you need to earn on the account to achieve this goal?
A) 4.5 percent
B) 5.5 percent
C) 6.5 percent
D) 8.5 percent

Accepted Answer

To find the rate needed, use the future value formula: FV = PV * (1 + r)^n. Plugging in the values: $1,450,000 = $300,000 * (1 + r)^25. Solving for r gives approximately 6.5%.

Question 17

Which of the following will not increase a present value?
A) increase the interest rate
B) decrease the number of periods
C) increase the future value

Accepted Answer

Increasing the interest rate actually decreases the present value of a future amount because the present value is inversely related to the interest rate. Higher interest rates mean a lower present value, as the discounting effect is stronger.

Question 18

Suppose a U.S. Treasury bond promises to pay $9,780.13 in three years. If bonds of this type are generating a 4 percent annual return, how much would you pay for this bond today?
A) $8,429.71
B) $11,001.32
C) $8,694.50
D) $9,112.78

Accepted Answer

To find the present value of the bond, you use the formula for present value: PV = FV / (1 + r)^n, where PV is the present value, FV is the future value ($9,780.13), r is the annual interest rate (0.04), and n is the number of years (3). Plugging in these values gives PV = $9,780.13 / (1 + 0.04)^3, which calculates to approximately $8,694.50.

Question 19

A $5,000 investment has doubled to $10,000 in ten years. How much longer will it take for the investment to reach $15,000 if it continues to earn the same rate?
A) 5.00 years
B) 5.85 years
C) 6.86 years
D) 7.20 years

Accepted Answer

The investment doubled ($5,000 to $10,000) in 10 years, indicating a 100% growth over this period. To find the annual growth rate, we can use the rule of 72, which estimates the number of years required to double an investment at a given annual rate. The formula is 72 / annual rate = years to double. Here, we have 72 / 10 = 7.2% as the approximate annual growth rate. To grow from $10,000 to $15,000 (a 50% increase) at a 7.2% annual rate, we can use the rule of 72 in reverse or directly calculate the time it takes for a 50% growth. Direct calculation or approximation methods show it takes slightly less than 6 years, making 5.85 years the closest and correct choice.

Question 20

What is the value in year 20 of a $1,000 cash flow made in year 8 if interest rates are 15 percent in years "6 through 13" and increase to 18 percent in the remaining years?
A) $5,779.57
B) $5,912.42
C) $6,005.71
D) $6,407.13

Accepted Answer

The answer of What is the value in year 20...

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

A firm's net income last year was $2.65 million. Its net income grew 8 percent during the last "5" years. If that growth rate continues, how long will it take for the firm's net income to double?

Which of the following is the equivalent of $300 received today?

What is the value in year 10 of a $1,000 cash flow made in year 5 if interest rates are 9 percent in years 6 and 7, and increase to 13 percent in the remaining years?

You invested $1,000 for five years in an account that earns 5 percent. However, today you learn that you are able to move the account into an investment that earns 10 percent. Which of the following statements is correct?

When your investment compounds, your money will grow in a(n) ________ fashion.

Which of the following statements is incorrect with respect to time lines?

A firm's net income last year was $1.5 million. Its net income grew 5 percent during the last "5" years. If that growth rate continues, how long will it take for the firm's net income to double?

A $1,000 investment has doubled to $2,000 in seven years. How much longer will it take for the investment to reach $5,000 if it continues to earn the same rate?

Which of the following investments would you prefer?

What is the value in year 6 of a $9,000 cash flow made in year 14 if interest rates are 7 percent in years "4 through 9" and increase to 10 percent after that?

You want to retire in 40 years and you have $40,000 saved in your retirement account. You believe you will need $1,500,000 upon retirement. What rate will you need to earn on the account to achieve this goal?

Which of the following would you prefer?

What is the value in year 4 of a $9,000 cash flow made in year 13 if interest rates are 7 percent in years "4 through 9" and increase to 11 percent after that?

Which of the following would you prefer?

A $400 investment has doubled to $800 in six years because of a 12.25 percent return. How much longer will it take for the investment to reach $1100 if it continues to earn 12.25 percent?

You want to retire in 25 years and you have just inherited $300,000. You believe you will need $1,450,000 upon retirement. What rate will you need to earn on the account to achieve this goal?

Which of the following will not increase a present value?

Suppose a U.S. Treasury bond promises to pay $9,780.13 in three years. If bonds of this type are generating a 4 percent annual return, how much would you pay for this bond today?

A $5,000 investment has doubled to $10,000 in ten years. How much longer will it take for the investment to reach $15,000 if it continues to earn the same rate?

What is the value in year 20 of a $1,000 cash flow made in year 8 if interest rates are 15 percent in years "6 through 13" and increase to 18 percent in the remaining years?