Question

Fair Insurance Ltd. is selling a 36-year annuity that will pay the annuitant of$60,000 at the end of each of the next 18 years and thereafter it will pay $70,000 at the end of each of the remaining 18 years. The relevant interest rate of the annuity if 4% per annum throughout 36 years. Mr. Wilson wants to buy the annuity offered by Fair Insurance. What the maximum price he should be willing to pay for the annuity? 9. is

Answer 1

The maximum price is computed as shown below:

= $ 60,000 / 1.04 + $ 60,000 / 1.04² + $ 60,000 / 1.04³ + $ 60,000 / 1.04⁴ + $ 60,000 / 1.04⁵ + $ 60,000 / 1.04⁶ + $ 60,000 / 1.04⁷ + $ 60,000 / 1.04⁸ + $ 60,000 / 1.04⁹ + $ 60,000 / 1.04¹⁰ + $ 60,000 / 1.04¹¹ + $ 60,000 / 1.04¹² + $ 60,000 / 1.04¹³ + $ 60,000 / 1.04¹⁴ + $ 60,000 / 1.04¹⁵ + $ 60,000 / 1.04¹⁶ + $ 60,000 / 1.04¹⁷ + $ 60,000 / 1.04¹⁸ + $ 70,000 / 1.04¹⁹ + $ 70,000 / 1.04²⁰ + $ 70,000 / 1.04²¹ + $ 70,000 / 1.04²² + $ 70,000 / 1.04²³ + $ 70,000 / 1.04²⁴ + $ 70,000 / 1.04²⁵ + $ 70,000 / 1.04²⁶ + $ 70,000 / 1.04²⁷ + $ 70,000 / 1.04²⁸ + $ 70,000 / 1.04²⁹ + $ 70,000 / 1.04³⁰ + $ 70,000 / 1.04³¹ + $ 70,000 / 1.04³² + $ 70,000 / 1.04³³ + $ 70,000 / 1.04³⁴ + $ 70,000 / 1.04³⁵ + $ 70,000 / 1.04³⁶

= $ 1,196,986.767

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