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:

After the child's sixth birthday, no more payments are made. When the child reaches age $65,$ he or she receives $$230,000.$

If the relevant interest rate is $10$ percent for the first six years and $6$ 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$.,32\mathrm{.}16.$

This is tricky! I suggest using Excel. It is easiest if you first figure out the future value of each cash flow at the end of year $6.$

Remember, the payments into the policy are at the end of the year, so when the question says the interest rate is $x\%$ for six years,

you need to determine how many years into the future there are for each cash flow. For instance, do you need to find the future

value of the first cash flow for five years or six years? Once you get the total of the future values of all cash flows at the end of

year $6,$ then you have to determine what that total is worth at year the child recelves the money.

Child's $65$th birthday