Question

a. Suppose a 65-year-old person wants to purchase an annuity from an insurance company that would pay $21,700 per year until the end of that person's life. The insurance company expects this person to live for 15 more years and would be willing to pay 7 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 $21,700 annuity, but this person is healthier and is expected to live for 20 more years. If the same 7 percent interest rate applies, how much should this healthier person be charged for the annuity? c. In each case, what is the new purchase price of the annuity if the distribution payments are made at the beginning of the year? (For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16)) a. Purchase price of the annuity b. Purchase price of the annuity c. 15-year purchase price 20-year purchase price

Answer 1

a. Purchase price of the annuity - 197641.73

b. Purchase price of the annuity - 229890.11

c. 15 year purchase price - 211476.66 and 20 year purchase price - 245982.42

Kindly refer to the images. The negative sign in the images is because that particular amount has to be paid by the person to the insurance company.
Function Arguments 7 X PV 0.07 Rate Nper Pmt 7% 200 T 20 21700 21700 FV = number Type = number = -229890. 1091 Returns the present value of an investment: the total amount that a series of future payments is worth now. Nper is the total number of payment periods in an investment. Formula result = -229890.1091 Help on this function OK Cancel

Function Arguments 7 x PV Rate 7% = 0.07 Nper 15 = 15 Pmt 21700 = 21700 Fv = number Type -211476.6553 Returns the present value of an investment: the total amount that a series of future payments is worth now. Rate is the interest rate per period. For example, use 6%/4 for quarterly payments at 6% APR. Formula result = -211476.6553 Help on this function OK Cancel

Function Arguments PV Rate 0.07 Nper 20 = 20 Pmt 21700 21700 Fv number Type = -245982.4168 Returns the present value of an investment: the total amount that a series of future payments is worth now. Fv is the future value, or a cash balance you want to attain after the last payment is made. Formula result = -245982. 4168

LLLLLL Function Arguments 7 X PV Rate 7% = 0.07 Nper 15 21700 21700 FV = number = number Type F = -197641.7339 Returns the present value of an investment: the total amount that a series of future payments is worth now. Rate is the interest rate per period. For example, use 6%/4 for quarterly payments at 6% APR. Formula result = -197641.7339 Help on this function ОК, Cancel