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.)

3a.

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

3b

Assume you can earn 6% interest (APR) on your savings, and you make a deposit in your savings account quarterly. How much do you need to save each quarter (every three months) in order to reach your goal, if you make your deposit at the beginning of each month? Briefly show your calculations.

Answer 1

Amount required in 5 years = FV = $20000

Number of quarters = n = 5*4 = 20 quarters

Quarterly Interest Rate = r = 0.06/4 = 0.015

Let the amount deposited each quarter be P

(3a) Amount is deposited at end of each quarter

=> FV = P(1+r)^n-1 +....+ P(1+r)² + P(1+r) + P = P[(1+r)ⁿ -1]/r

=> 20000 = P[(1+0.015)²⁰ -1]/0.015

=> P = 20000*0.015/[(1+0.015)²⁰ -1] = $864.91

(3b) Amount is deposited at beginning of each quarter

FV = P(1+r)ⁿ +....+ P(1+r)² + P(1+r) = P [((1 + r)ⁿ - 1) / r](1 + r)

=> 20000 = P [((1 + 0.015)²⁰ - 1) / 0.015](1 + 0.015)

=> P = 20000*(1+0.015) / [((1 + 0.015)²⁰ - 1) / 0.015] = $877.89