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: ........... $ 700
Second birthday: ............ $ 700
Third birthday: ............ $ 800
Fourth birthday: .......... $ 800
Fifth birthday: ............ $ 900
Sixth birthday: ............ $ 900
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?