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: Second birthday: Third birthday: Fourth birthday: Fifth birthday: Sixth birthday: $ $ $ $ $ $ 860 860 960 960 1,060 1,060 After the child's sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $120,000. If the relevant interest rate is 9 percent for the first six years and 5 percent for all subsequent years, what is the value of the policy at the child's 65th birthday? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Child's 65th birthday

Explanation / Answer

value on the 6th birthday = 860*1.09^5 + 860*1.09^4 + 960*1.09^3 + 960*1.09^2 + 1060*1.09 + 1060 = 7136.3806

value on the 65th birthday = 7136.3806 * 1.05^59 + 120,000 = 246,954.08

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