Please show work 3. (a) You are saving for retirement, and you can afford to save $22,500 every year, starting one year from today. If you invest for 30 years at an annual interest rate of 4.50% per year, how much will you have saved for your retirement? Hint, this is the FV of an annuity. You may want to solve parts (c) and (e), then come back and solve (b) and (d), which are annuities due.

(b) How much would you have in your retirement account if you began these same 30 annual payments immediately? Hint: This is now the FV of an annuity due.

c) Now let's look at things a little differently. Suppose that once you retire, you want to be able to withdraw $85,000 per year (starting one year from your retirement) for a total of 25 years during your retirement. How much would you need to have in your account when you retire to make this work assuming an annual interest rate of 4.50%? Hint: This is the PV of an annuity.

(d) How much would you need to have in your retirement account if you began these same 25 annual withdrawals immediately? Hint: This is now the PV of an annuity due. Reset your calculator to END of period payments when you have finished the annuity due problems.

(e) Let's assume that you want to have $2,250,000 in your retirement account at the end of 30 years. You have now decided that you will deposit funds at the end of every month for 30 years. The interest rate is 4.50% (APR). How much do you need to deposit each month?