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:

After the child's $6$th birthday, no more payments are made. When the child reaches age $65,$ he or

she receives $$1,000,000.$ If the relevant interest rate is $15\%$ for the first six years and $12\%$ for all

subsequent years, is the policy worth buying? Why? $(6$ marks$)$