Question

Professor’s Annuity Corp. offers a lifetime annuity to retiring professors. For a payment of $21,000 at age 70, the firm will pay the retiring professor $2,250 a semi-annual until death. If the professor’s remaining life expectancy is 10 years, what is effective annual interest rate on this annuity?

1.28%

11.32%

8.69%

17.38%

Answer 1

PV of annuity = $21000

Semiannual payment = $2250

total payments 20

PV of an ordinary annuity can be calculated using formula

PV = A*(r/n)/(1 - (1+r/n)^(-n*t))

So, 21000 = 2250*(r/2)/(1 - (1+r/2)^(-20))

So, r = 8.69%

So annual interest rate = 2*8.69 = 17.38%