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 childs 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 $400

Second birthday $500

Third birthday $ 600

Fourth birthday $700

Fifth birthday $800

Sixth birthday $900

After the childs sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $250,000. 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? (explain with a equation as well)