a. Suppose a 65-year-old person wants to purchase an annuity from an insurance c

Question

a. Suppose a 65-year-old person wants to purchase an annuity from an insurance company that would pay $20,000 per year until the end of that person's life. The insurance company expects this person to life for 15 more years and would be willing to pay 6 percent on the annuity. How much should the insurance company ask this person to pay for the annuity? b. A second 65-year-old person wants the same $20,000 annuity, but this person is healthier and is expected to life for 20 more years. If the same 6 percent interest rate applies, how much should this healthier person be charged for the annuity? c. In each case, what is the difference in the purchase price of the annuity if the distribution payments are made at the beginning of the year?

Explanation / Answer

Part A

Lumpsum (PV) = Annuity * pvifa (6%,15years) = 20000*((1-((1.06^-15)))/6%) = 194,248.98

Part B

Lumpsum (PV) = Annuity * pvifa (6%,20years) = 20000*((1-((1.06^-20)))/6%) = 229,398.42

Part C

1. Lumpsum (PV) = Annuity *( pvifa (6%,15years) *(1.06)) =20000*(((1-((1.06^-15))/6%)*1.06)) = 205,899.68

2. Lumpsum (PV) = Annuity * (pvifa(6%,20years) *(1.06)) = 20000*(((1-((1.06^-20))/6%)*(1.06)) = 243,162.33

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