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: ........$ 500
Second birthday: .........$ 600
Third birthday: .........$ 700
Fourth birthday: .......$ 800
Fifth birthday: .........$ 900
Sixth birthday: ........$ 1,000
After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $ 275,000. If the relevant interest rate is 11 percent for the first six years and 7 percent for all subsequent years, is the policy worth buying?