Problem 1 Start Saving now

(Note: You must show all your calculations. You are not allowed to use Excel Solver or any other Excel add-in formulas. You have to use formulas we learned and derived in the class. Round all your answers to 2 decimal points)

After successfully passing Corporate Finance course, you decide to start saving for your retirement.

You open a savings account with an interest of 12% per annum APR with monthly compounding (thus the effective monthly interest rate is 12% 12 = 1%).

Over the next 35 years, at the end of each month, you deposit $50 into your deposit account.

a) How much money will you have immediately after your last deposit? (5 points)

Now assume 35 years have passed (you deposited promptly each month for 35 years!) and you retired.

Nevertheless, you expect to have an active life during the next 25 years of your life.

2. How much money can you withdraw from your deposit each month over the next 25 years? (5 points)

3. Now think that you want to withdraw $1 000 each month over the next 25 years once you are retired (after 35 years). In order to be able to do so, how much you need to deposit monthly in years 1 35?

(10 points)

4. Think again about task c) Withdrawing equal amount may not be optimal because of inflation: money loses its value over time. Suppose you expect average inflation to be 3% per year (accrued gradually throughout each year). Find the deposit amount that gives you $1 000 monthly withdrawal at real prices. Thus, the first withdrawal will be $1 000, the next withdrawal will be increased by one-month inflation etc. (Assume the deposit amount is constant and is not adjusted for inflation) (10 points)

Hint to solve the Problem 1: Draw a timeline for each part. Make sure you understand that you have monthly deposit and withdrawals. Distinguish between PV, FV. Think a minute and you find this problem very easy.

30 points

Problem 2 Save Smart

Compute EAR for the following (show clearly all your calculations, round answers to 2 decimal points):

1. 7% APR compounded monthly (5 points)

2. 8% APR compounded quarterly (5 points)

3. 11% APR compounded annually (5 points)

4. 6% APR compounded daily (assume that there are 365 days in the year) (5 points)

20 points