Question

6. You are graduating in two months and already have a job. You are planning to buy a $250,000 house immediately upon graduation. Since you have been frugal during your college years and you attend the best college value in America, you have saved $10,000, which you will use as a down payment. You have locked in an interest rate of 6% compounded monthly and you plan to pay for the house over 20 years. Your first payment is due one month after closing on the house.

1. After you have made 3/4^th of the payments, what percent of the original loan remains to be paid?
2. How many payments must be made before you have paid back over half the amount you borrowed? SET UP THE EXPRESSION ONLY.

Answer 1

loan = 250000 - 10000 = 240000

I = 6% = 6%/12 = 0.5% per month

t = 20 years = 20 * 12 = 240 months

Monthly payments = 240000*(A/P,0.5%,240) = 240000*0.0071643 = 1719.432

a. 3/4 payments already done, payment periods left = 1/4 * 240 = 60

Principal due = 1719.432 * (P/A,0.5%,60) = 1719.432 * 51.725560 = 88938.58

principal due (%) = 88938.58 / 240000 * 100 = 37.0577% = 37.06%

b. half the amount = 240000/2 = 120000

Let no. of periods left after paying half of amount is n, then

120000 = 1719.432 * [((1 + 0.005)^n-1)/(0.005*(1 + 0.005)^n)]

[((1.005)^n-1)/(0.005*(1.005)^n)] = 69.790488

After solving for n, from the above expression, subtract n from 240, and you will get the period required for paying half of the principal