# Time Value of Money

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1. Your younger sister, Jennifer, will start college in five years. She has just informed your parents that she wants to go to Chapman University, which will cost $50,000 per year for four years (cost assumed to come at the beginning of each year). Anticipating Jennifer’s ambitions, your parents started investing $10,000 per year five years ago, just made another $10,000 deposit, and will continue to make annual deposits for five more years.

How much more will your parents have to invest at the end of each year for the next five years to have the necessary funds for Jennifers’s education? Use 5 percent as the appropriate interest rate throughout this problem (for discounting or compounding). Round all values to whole numbers.

HINT: First calculate the amount that will be needed in 5 years to pay all four years of tuition. Note that the payments for tuition come at the beginning of each year. Then calculate how much your parents have now. Then enter the amount your parents have now as PV (negative), the amount needed in 5 years for tuition as FV (positive), n = 5, and i =5%, and solve for PMT.

2. Five years have passed and Jennifer is now 18 years old. Your parents have accumulated the necessary funds for her education. However, your sister wants to start a business instead of going to college.

Instead of her schooling, your parents are giving Jennifer $40,000 to help her start a business and the parents plan to take year-end vacations costing $8,000 per year for the next three years. Use 10 percent as the appropriate interest rate throughout the problem.

a. How much money will your parents have at the end of three years to help you with graduate school, which you will start then?

HINT: Enter the amount that was accumulated for college costs minus the cost of the business start-up as PV (negative), the cost of the vacations as PMT (positive), i = 10%, n = 3, and solve for FV.

b. You plan to work on a master’s and perhaps a Ph.D. If graduate school costs $38,600 per year, approximately how long will you be able to stay in school based on these funds?

HINT: Enter the amount your parents will have for you to go to graduate school as PV (negative), the annual cost of school as PMT (positive), 1 = 10%, and solve for n.

3. You are 21 years old and plan to retire in 34 years. After you retire you expect to live for 35 years. You want a fixed retirement income that has the same purchasing power at the time you retire as $100,000 has today (you realize that the real value of your retirement income will decline year by year after you retire). Your retirement income will begin the day you retire, 34 years from today. Inflation is expected to be 3 percent per year from today forward, you currently have $10,000 saved up, and you expect to earn a nominal annual return on your savings of 10 percent per year. To the nearest dollar, how much must you save during each of the next 34 years (with deposits being made at the end of each year) to meet your retirement goal?

HINT: First calculate the amount that you want to receive each year during retirement. This is $100,000(1.03)34. This becomes the PMT for each year during retirement. Calculate the present value of this amount as of the day you retire. Then enter this number as FV (positive), the amount you have saved as PV (negative), n=34 and compute payment.

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