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. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Explanation / Answer

Answer:We need to find the FV of the Premiums to compare With the cash payments 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=1223.99

FV2=$760(1.10)^4=1112.72

FV3=$860(1.10)^3=1144.66

FV4=$850(1.10)^2=1028.50

FV5=$960(1.10)^1=1056

Value at year 6=1223.99+1112.72+1144.66+1028.5+1056+950=6515.87

Finding the FV of this lumpsum at the child's 65th Birthday:

FV=$6515.87*(1.07)^59=352870.45

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