Question

An investment offers $5,500 per year, with the first payment occurring one year from now. The required return is 7 percent. a. What would the value be today if the payments occurred for 20 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What would the value be today if the payments occurred for 45 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. What would the value be today if the payments occurred for 70 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) d. What would the value be today if the payments occurred forever? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

a. What would the value be today if the payments occurred for 20 years?

this is an ordinary annuity, so we can use the present value of an ordinary annuity formula:

present value = annuity payment x annuity factor

• annuity payment = $5,500
• PV annuity factor, 7%, 20 periods = 10.594

present value = $5,500 x 10.594 = $58,267

b. What would the value be today if the payments occurred for 45 years?

present value = annuity payment x annuity factor

• annuity payment = $5,500
• PV annuity factor, 7%, 45 periods = 13.60552

present value = $5,500 x 13.60552 = $74,830.36

c. What would the value be today if the payments occurred for 70 years?

present value = annuity payment x annuity factor

• annuity payment = $5,500
• PV annuity factor, 7%, 70 periods = 14.16039

present value = $5,500 x 13.60552 = $77,882.25

d. What would the value be today if the payments occurred forever?

we must use the perpetuity formula:

present value = $5,500 / 7% = $78,571.43