Question 1: Future Values and Policy Evaluation (10 points) An insurance company

Question

Question 1: Future Values and Policy Evaluation (10 points)
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 $ 1,020

Fourth birthday$850

Fifth birthday $ 1,120
Sixth birthday $950

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 13 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? Is the policy worth buying?

Explanation / Answer

To compare $420,000 we need to calculate future value of payments till 65th year.

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Future value of series of payments = 920 x (1+13%)^5 + 920 x (1+13%)^4 + 1020 x (1+13%)^3 + 850 x (1+13%)^2 + 1120 x (1+13%)^1 + 950 x (1+13%)^0

Future value of series of payments = $7,967.7960

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Now, we can calculate the future value of the series of payment for balance years 59 years (65 years - 6 Years):

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Future value at 65th years = Future value of series of payments x (1+ Applied rate)^Balance years

Future value at 65th years = 7,967.7960 x (1+7%)^59

Future value at 65th years = $431,500.29

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The calculated value i.e. $431,500.29 is more than the offered value of $420,000 hence, policy is not worth buys since calculated value is more than offered value.

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