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

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:

After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $300,000. If the relevant interest rate is 10 percent for the first six years and 7 percent for all subsequent years, what would the value of the deposits be when the policy matures?

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:

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 = $800(1.10)5 = $1,288.408

FV2 = $800(1.10)4 = $1,171.28

FV3 = $900(1.10)3 = $1,197.9

FV4 = $850(1.10)2 = $1,028.50

FV5 = $1000(1.10)1 = $1,100.00

FV6=$950 (1.10)0=$950

Value at year six = $1,288.408 + 1,171.28 + 1,197.9 + 1,028.50 + 1,100.00 + 950 = $6736.088

Finding the FV of this lump sum at the child's 65th birthday:  

FV = $6,736.088(1.07)59 = $364,796.5

The policy is not worth buying the future value of the policy is $364,796.5 , but the policy contract will pay off $300,000. The premiums are worth $64796.5 more than the policy payoff.

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