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 payment 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$$s sixth birthday, no more payments are made. When the child reaches age $65,$ he or she receives $$350,000.$ If the relevant interest rate is $10$ percent for the first six years and $7$ percent for all subsequent years, is the policy worth buying?