Q: A growing annuity pays $$C in $$the first period and grows at rate $$g$$ for $$N$$ periods. Which formula gives the present value if the discount rate is $$r$$?

$$PV = C \times \frac{1 - ((1 + g)/(1 + r))^N}{r - g}$$

Question 1

Which of the following best describes the rule for combining cash flows when valuing a stream of cash flows?

Accepted Answer

Only cash flows at the same point in time can be compared or combined.

Question 2

Suppose you deposit $$1,000 today and 1$$,000 at the end of each of the next two years in an account earning 10% interest. What is the future value of your savings at the end of year 3?

Accepted Answer

$3,641

Question 3

Given the following cash flows: $$5,000 in one year, 8$$,000 in each of the next three years, and a discount rate of 6%, what is the present value of these cash flows? Use the formula $$PV = \frac{C_1$}{(1+r)^1$} + \frac{C_2$}{(1+r)^2$} + \frac{C_3$}{(1+r)^3$} + \frac{C_4$}{(1+r)^4$}.$$

Accepted Answer

$24,890.65

Question 4

Which formula correctly expresses the present value of a perpetuity with payment $$C$$ and interest rate $$r$$?

Accepted Answer

$$PV = \frac{C}{r}$$

Question 5

You want to endow a graduation party costing $$30,000 per year forever. If the university earns 8% per year, how much must you donate today? Use PV$$ = \frac{C}{r}$.

Accepted Answer

$375,000

Question 6

Which of the following is the main difference between an annuity and a perpetuity?

Accepted Answer

An annuity has a fixed number of payments, while a perpetuity lasts forever.

Question 7

You win a lottery that pays $$1 million per year for 30 years (first payment today) or 15 $$million today. If the interest rate is 8%, what is the present value of the 30 payments? (Hint: Use the annuity formula for 29 payments and add the first payment.)

Accepted Answer

$12.16 million

Question 8

Ellen saves $$10,000 at the end of each year for 30 years in an account earning 10% interest. What is the future value of her savings at retirement? Use FV = $$PMT 	imes \frac{(1 + r)^N - 1}{r}$.

Accepted Answer

$1,644,940

Question 9

A growing perpetuity pays $$C in $$the first period and grows at rate $$g$$ each period. What is the present value formula if the discount rate is $$r$$ and $$r \u003e g$$?

Accepted Answer

$$PV = \frac{C}{r - g}$$

Question 10

Your firm borrows $$80,000 for 30 years at 8% interest. What is the annual loan payment? Use the annuity payment formula C = PV$$ 	imes \frac{r}{1 - (1 + $$r)^{-N}$$}$.

Accepted Answer

$7,106.19

Question 11

Suppose you invest $$20,000 at 8% interest for 15 years. What is the future value? Use FV = PV$$ 	imes (1 + r)^N$.

Accepted Answer

$63,443

Question 12

If you have $$10,050 saved and add 5$$,000 per year at 7.25% interest, how many years will it take to reach $60,000? (Use the annuity and compound interest formulas.)

Accepted Answer

7 years

Question 13

Which of the following is NOT a variable commonly used in financial calculators for time value of money problems?

Accepted Answer

ROI

Question 14

If you want to solve for the interest rate that equates a $$1,000 investment today with a 2$$,000 payoff in 6 years, which equation would you use?

Accepted Answer

$$1,000 = \frac{2,000}{(1 + r)^6$}$$

Question 15

A growing annuity pays $$C in $$the first period and grows at rate $$g$$ for $$N$$ periods. Which formula gives the present value if the discount rate is $$r$$?

Accepted Answer

$$PV = C 	imes \frac{1 - ((1 + g)/(1 + r))^N}{r - g}$$

Question 16

If you are offered either $$15 million today or 30 annual payments of 1 $$million (first payment today), what is the minimum rate of return you must earn to make the lump sum more attractive? (Use the annuity formula and solve for $$r.)$$

Accepted Answer

5.72%

Question 17

Which of the following statements about the time value of money is TRUE?

Accepted Answer

The present value of a future cash flow decreases as the discount rate increases.

Time Value of Money: Streams of Cash Flows, Perpetuities, Annuities, and Variable Solving

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