An individual has just received a settlement form the insurance company of $500,

Question

An individual has just received a settlement form the insurance company of $500,000. He decides to invest the entire amount into a Treasury note for 10 years paying 4% annual interest (compounded semi-annually). After the ten years, the individual wishes to purchase and annuity and receive monthly payments for 30 years. Assume the annuity will pay 5% annual interest. A) What would be the monthly payments? B) How much interest for the entire period will he have received?   (Count both the 10 year Treasury and the 30 year annuity).

Explanation / Answer

Value of investment after 10 years into Treasury note = $500,000 * (1 + 4%/2)10*2

= $742,973.70

(A) Value of annuity today = Monthly payment to be received * [1 - (1 + 5%/12)-30*12] / (5%/12)

=> $742,973.70 = Monthly payment to be received * 186.2816

=> Monthly payment to be received = $3,988.44

(B) Total interest = $3,988.44 * 360 - $500,000

= $935,839.65

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