Professor’s Annuity Corp. offers a lifetime annuity to retiring professors. For

Question

Professor’s Annuity Corp. offers a lifetime annuity to retiring professors. For a payment of $89,000 at age 65, the firm will pay the retiring professor $825 a month until death.

a. If the professor’s remaining life expectancy is 20 years, what is the monthly interest rate on this annuity? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

b. What is the effective annual interest rate? (Use the monthly rate computed in part (a) rounded to 2 decimal places when expressed as a percent. Enter your answer as a percent rounded to 2 decimal places.)

c. If the monthly interest rate is 0.50%, what monthly annuity payment can the firm offer to the retiring professor? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Explanation / Answer

Answer a.

Cost of Annuity = $89,000
Monthly Payment = $825
Period = 20 years or 240 months

Let monthly interest rate be i%

$89,000 = $825 * PVIFA(i%, 240)

Using financial calculator:
N = 240
PV = -89000
PMT = 825
FV = 0

I = 0.79%

Monthly interest rate = 0.79%

Answer b.

Effective Annual Interest Rate = (1 + Monthly interest rate)^12 - 1
Effective Annual Interest Rate = (1 + 0.0079)^12 - 1
Effective Annual Interest Rate = 1.0079^12 - 1
Effective Annual Interest Rate = 1.0990 - 1
Effective Annual Interest Rate = 0.0990 or 9.90%

Answer c.

Cost of Annuity = $89,000
Period = 20 years or 240 months
Monthly interest rate = 0.50%

$89,000 = Monthly Payment * PVIFA(0.50%, 240)
$89,000 = Monthly Payment * (1 - (1/1.005)^240) / 0.005
$89,000 = Monthly Payment * 139.58077
Monthly Payment = $637.62

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