Question

A 55 -year-old man deposits $50,000 to fund an annuity with an insurance company. The money will be invested at 8 % per year, compounded semiannually. He is to draw semiannual payments until he reaches age 65. What is the amount of each payment?

Answer 1

To calculate the semiannual payments from an annuity, use the present value of an annuity formula with a present value of $50,000, a semiannual interest rate of 4% (since the annual rate is 8% and compounded semiannually), and 20 total payments over 10 years.

Step-by-step explanation:

The question requires calculating the semiannual payments that a 55-year-old man would receive from an annuity after making a deposit of $50,000 with an 8% annual rate that is compounded semiannually until he reaches the age of 65.

To find the amount of each semiannual payment, we first need to determine the number of payments. The man will receive payments for 10 years, and since the payments are semiannual, there will be a total of 10 * 2 = 20 payments. The interest rate per period is 8% per year, or 4% semiannually, since it is compounded semiannually.

Using the formula for the present value of an annuity:

Present Value of Annuity = Payment * [(1 - (1 + r)^(-n)) / r]

Here 'r' is the interest rate per period and 'n' is the total number of payments. Substituting the given values:

50,000 = Payment * [(1 - (1 + 0.04)^(-20)) / 0.04]

Solving this equation, we find the value of the Payment, which is the amount of each semiannual payment that will be received.