(Solved): You are 20 years old today. When you turn 62 , you want to retire. Starting on your 62nd birthday ...

You are 20 years old today. When you turn 62 , you want to retire. Starting on your $62^{\text{nd }}$ birthday you want to receive funds from a growing annuity; the first payment would be $\$60,000$ and grow at a rate of $5\%$ per year for a total of 35 payments (including the first one). Your plan is to start saving for this plan on your $24^{\text{th }}$ birthday; your first deposit would be $\$6,386.27$ and would stay constant for a total of 25 deposits. On your $55^{\text{th }}$ birthday, you calculate the amount of your compounded savings have and need to determine whether you have enough saving or not. On that $55^{\text{th }}$ birthday, how much are you over funded (and can take money out and still have enough in the account to fund your planned annuity!)? Assume a discount rate (or rate of return) of $8\%$ for all periods. $\begin{array}{l}\$492,000\\ \$125,000\\ \$5,000\\ \$250,000\\ \$175,000\\ \$10,000\end{array}$