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%
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%
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