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 $87,000 at age 65, the firm will pay the retiring professor $775 a month until death.

a. If the professor’s remaining life expectancy is 15 years, what is the monthly interest rate on this annuity? What is the effective annual rate?

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 .75%, what monthly annuity payment can the firm offer to the retiring professor?

Monthy annuity payment = $ ___________

Explanation / Answer

PV of the Annuity is $87000 Formula for Present value of Annuity = PV= A*[(1+k)^n-1]/k(1+k)^n A=775 per month n=15 yrs=15*12=180 month Assume k is the interest rate   87000= 775*[(1+k)^180-1]/k(1+k)^180 [(1+k)^180-1]/k(1+k)^180 =112.26 k=0.5716% per month So Required monthly interest rate = 0.5716% Annual Interest rate = 6.86% Effective Annual Rate =(1+0.0686/12)^12-1= 7.080% So EAR =7.08 % When monthly interest rate =0.75% , then ,Assume monthly payment =A 87000=A*[(1.0075^180-1]/0.0075*(1.0075)^180 A =882.41 So in this situation monthly payment would be $882.41

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