Your youngest daughter will be starting college in $14$ years. Currently the cost for college is $$25,000$ per year and cost is expected to increase at $g=6\%$ per year. You would like to fully fund her college cost by making $8$ equal annual payments, with the first payment today. If you can earn $9\%,$ how much must you deposit each year, starting today, in order to have enough money to pay for college beginning in Year $14.$ Assume that your account will continue to earn the $9\%$ even after you stop contributing. Round final answers to $2$ decimal places. Show your work in detail for full credit.

Hint:

This problem involves a growing annuity.

Step $1$: Calculate the cost of college in the $1^{st}$ year of study $($FV$)$

Step $2$: Find the PV of the growing annuity $($total cost of $4-$year college, at the beginning of college$)$

Step $3$: Find the PV of the above sum, $6$ years prior to college

Step $4$: Find the value of the $8$ equal annual payments $($PMT$)$ that will grow to the above sum in $8$ years