Question

You just graduated from college and decide to start saving for a down payment to buy a house 5 years from today. You estimate you will need $20,000 in 5 years for the down payment. (Note: a down payment is a deposit a home buyer must make in order to get a mortgage loan from a bank to buy the house.)

1. Assume you can earn 6% interest (APR) on your savings, and you want to make a single deposit today. How much do you need to deposit today in order to reach your goal? Briefly show your calculations.

2. Assume you can earn 6% interest (APR) on your savings, and you make a deposit in your savings account at the end of each year. How much do you need to save each year in order to reach your goal? Briefly show your calculations.

Answer 1

1)

Present value = Future value / (1 + r)ⁿ

Present value = 20,000 / (1 + 0.06)⁵

Present value = 20,000 / 1.338226

Present value = $14,945.16

You need to deposit $14,945.16

2)

Present value = Annuity * [1 - 1 / (1 + r)ⁿ]/ r

20,000 = Annuity * [1 - 1 / (1 + 0.06)⁵]/ 0.06

20,000 = Annuity * [1 - 0.747258] / 0.06

20,000 = Annuity * 4.212364

Annuity = $4,747.93

Each year should save $4,747.93