In: 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: $750 Second birthday: 750 Third birthday: 850 Fourth birthday: 850 Fifth birthday: 950 Sixth birthday: 950 After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $500,000. If the relevant interest rate is 10 percent for the first six years and 8 percent for all subsequent years, is the policy worth buying?
YEAR | VALUE AT YEAR 6 |
1 | ? |
2 | ? |
3 | ? |
4 | ? |
5 | ? |
6 | ? |
Total Value at Year 6 | ? |
Total Value at Year 65 | ? |
future value = present value * (1 + interest rate)number of years
We calculate the future value of each payment, compounded up to the child's 65th birthday
First, we calculate the future value of the payments as on 6th birthday using 10% interest rate.
Next, we calculate the future value of the payments as on 65th birthday using 8% interest rate.
Number of years from 6th birthday to 65th birthday = 59 years.
Total future value as on 65th birthday = $605,743
It is not worth buying the policy because the amount received from the insurance company on 65th birthday ($500,000) is lower than the total future value of payments ($605,743)