Question

At retirement in December, you buy a special type of insurance policy called an immediate term annuity. This policy promises to pay the holder (or the holder’s heirs) $25,000 per year for the next 29 years. Each payment is at the start of the year. (Hence, the first payment will be very shortly after purchase of the policy.) The appropriate discount rate is 4.28% per year, compounded annually. What is the value of this policy to the policy holder?

Do not round at intermediate steps in your calculation. Report your answer in dollars. Enter your answer without the $ symbol.

Answer 1

Annual payment = $25,000
Number of payments = 29
Annual discount rate = 4.28%

Present value of policy = $25,000 + $25,000/1.0428 + …. + $25,000/1.0428^27 + $25,000/1.0428^28
Present value of policy = $25,000 * 1.0428 * (1 - (1/1.0428)^29) / 0.0428
Present value of policy = $25,000 * 17.137993
Present value of policy = $428,449.83

So, the value of this policy to the policy holder is $428,449.83 or $428,450