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: .....................$ 800
Second birthday: ...............$ 800
Third birthday: ..................$ 900
Fourth birthday: ...............$ 900
Fifth birthday: ................$1,000
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 $150,000. If the relevant interest rate is 10 percent for the first six years and 5.75 percent for all subsequent years, is the policy worth buying?