Problem $5-60$ Future Value and Multiple Cash Flows $[$LO $1]$

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: $ $880$

Second birthday: $ $880$

Third birthday: $ $980$

Fourth birthday: $ $980$

Fifth birthday: $ $1,080$

Sixth birthday: $ $1,080$

After the child$$s sixth birthday, no more payments are made. When the child reaches age $65,$ he or she receives $$420,000.$

If the relevant interest rate is $12$ percent for the first six years and $7$ percent for all subsequent years, what is the value of the policy at the child's $65$th birthday?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$