An insurance company is offering a new policy to its customers. Typically, the p

Question

An insurance company is offering a new policy to its customers. Typically, the policy is bought by a parent or grandparent for a child at the child’s birth. The details of the policy are as follows: The purchaser (say, the parent) makes the following six payments to the insurance company:

First birthday: $ 760

Second birthday: $ 760

Third birthday: $ 860

Fourth birthday: $ 850

Fifth birthday: $ 960

Sixth birthday: $ 950

After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $260,000. The relevant interest rate is 10 percent for the first six years and 7 percent for all subsequent years.

Find the future value of the payments at the child's 65th birthday: Future Value $____________

Explanation / Answer

Answer:

We need to find the FV of the premiums to compare with the cash payment promised at age 65. We have to find the value of the premiums at year 6 first since the interest rate changes at that time. So:

FV1 = $760(1.10)5 = $1,223.99

Future Value = $6,515.87(1.07)59 = $352,870.55.

The policy is not worth buying; the future value of the deposits is $352,870.55, but the policy contract will pay off $260,000. The premiums are worth $92,870.55 more than the policy payoff.

We need to find the FV of the premiums to compare with the cash payment promised at age 65. We have to find the value of the premiums at year 6 first since the interest rate changes at that time. So:

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