Finance

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: $920
Second birthday:920
Third birthday: 1020
Fourth birthday: 1020
Fifth birthday: 1,120
Sixth birthday: 1,120

After the child's sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $430,000. The relevant interest rate is 12 percent for the first 6 years and 7 percent for all subsequent years. What is the value of the policy at the child's 65th birthday?

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  1. Value at the end of 6 years
    = 1120 + 1120(1.12) + 1020(1.12)^2 + 1020(1.12)^3 + 920(1.12)^4 + 920(1.12)^5
    = 8155.91

    now the rate goes down to 7% for the next
    59 years.
    Final value at age 65
    = 8155.91(1.07)^59
    = 441,687.52

    but they only paid out $430,000
    while using that money to invest in other business ventures. Mmmmh, can you see why "insurance" is a profitable business to be in?

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  2. Hi Reiny,

    I came up with the same answer using the same logic you did. Unfortunately, I am doing this question through an online system that checks my answer automatically, and the system says that the answer is wrong. I have tried every variation that I can think of, and still can't come up with the right answer. :( Any other ideas?

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  3. Never mind!!! It helps to put the answer to the correct question! :)

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