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: $ 880 Second birthday: $ 880 Third birthday: $ 980 Fourth birthday: $ 980 Fifth birthday: $ 1,080 Sixth birthday: $ 1,080 After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $420,000. If the relevant interest rate is 12 percent for the first six years and 7 percent for all subsequent years, what is the value of the policy at the child's 65th birthday?

Explanation / Answer

We have to find the FV of the premiums to compare with the cash payment promised at age 65. We have to find the value of all the premiums at Year 6 first since the interest rate changes from that time.

So,

FV1= $880(1.12)5= $1,550.87

FV2= $880(1.12)4= $1,384.7

FV3= $980(1.12)3= $1,376.83

FV4= $980(1.12)2= $1,229.31

FV5= $1,080(1.12)1= $1,209.6

Value at Year 6 = $1,550.87 + 1,384.7 + 1,376.83 + 1,229.31 + 1,209.60 + 1,080 = $7,831.31

Calculating the FV of this lump sum at the child’s 65th birthday:

FV = $7,831.31(1.07)59= $424,108.81

The policy is not worth buying. The future value of the deposits is $424,108.81, but the policy contract will pay off $420,000. The premiums are worth $4,108.81 more than the policy payoff.

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