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 $77,000 at age 65, the firm will pay the retiring professor $525 a month until death. a. If the professor's remaining life expectancy is 15 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.) Monthly rate on annuity 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.) Effective annual rate% C. If the monthly interest rate is 075%, what monthly annuity payment can the firm offer to the retiring professor? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Monthly annuity payment

Explanation / Answer

Answer a.

Single Payment on age 65 = $77,000
Monthly payment = $525
Period = 15 years or 180 months

Let monthly interest rate be i%

$77,000 = $525 * PVIFA(i%, 180)

Using financial calculator:
N = 180
PV = -77000
PMT = 525
FV = 0

I = 0.23%

Monthly Rate on annuity = 0.23%

Answer b.

Monthly Rate = 0.23%

Effective Annual Rate = (1 + Monthly Rate)^12 - 1
Effective Annual Rate = (1 + 0.0023)^12 - 1
Effective Annual Rate = 1.0023^12 - 1
Effective Annual Rate = 1.0280 - 1
Effective Annual Rate = 0.0280 or 2.80%

Answer c.

Monthly Rate = 0.75%
Single Payment on age 65 = $77,000
Period = 15 years or 180 months

Monthly Payment * PVIFA(0.75%, 180) = $77,000
Monthly Payment * (1 - (1/1.0075)^180) / 0.0075 = $77,000
Monthly Payment * 98.59341 = $77,000
Monthly Payment = $780.99

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