Question

1. Retirement Savings After completing your MBA, you are committed to saving for retirement. To do so, you plan to maximize your contributions to your tax-deferred (401k) retirement account. You plan to invest your savings in low-cost equity mutual funds. In your opinion, this will give you an 8% effective annual rate of return. You plan to work 30 years, then retire. A. What is the APR with monthly compounding that will yield an effective annual rate of 8%?

B. If you contribute $1,000 to your retirement account each month, what will the value of your retirement account be 30 years from today? Assume your first deposit is made in one month and your last deposit is made on your retirement day—30 years from today. For this problem, assume a monthly interest rate of 65 bps (0.65%).

C. Assume you wait to save for retirement. Instead of starting in your first year of employment, you start 10 years later and save for 20 years (i.e., your first monthly deposit is 10 years and one month from today). What is the value of your retirement savings 30 years from today? For this problem, assume a monthly interest rate of 65 bps (0.65%).

D. Assume your retirement account is worth $1,000,000 on the date of your retirement. While you will continue to earn 65 bps per month on your investments, you plan to make monthly withdrawals while in retirement. Assuming you would like to make monthly withdrawals for the next 40 years (whereupon you promptly drop dead or become a ward of the state), how much can you withdraw from your retirement account each month?

Answer 1

Part A:

APR=((1+EAR)^(1/t)-1)*t

Where t= number of times compounded a year.

Since interest is compounded 12 times a year,

APR equivalent o EAR of 8%=((1+8%)^(1/12)-1)*12

=(1.08^ 0.083333-1)*12 = 7.720836%

Part B:

If the investment commences now (for 30 years), value of retirement account in 30 years from now =$1,431,219.17

Part C:

If the investment commences after 10 years (for 20 years), value of retirement account in 30 years from now= $574,593.63

Part D:

If the retirement account is worth $1,000,000 on the retirement date, monthly withdrawal during 40 years of retirement (assuming end-of-month withdrawals)= $6,803.47

Calculations as below: