Question

Person P got a house for $200,000 and made a $60,000 down payment. He obtained a 30 - year loan for the remaining amount. Payments were made monthly. The nominal annual interest rate was 6%. After 10 years (120 payments) he sold the house and paid off the loan’s remaining balance.

(a) What was his monthly loan payment?

(b) What must he have paid (in addition to his regular 120th monthly payment) to pay off the loan?

Answer 1

P made a down payment of $60,000. So the he obtained a loan for the remaining amount of $200000-$60000= $140000.

140000 = A (P/A, .5%, 360)

140000= 166.79*A

A= 140000/166.79

A= $839.38

His monthly loan payment is $839.38.

In 120 payments, amount paid by him: $839.38* 120 = $100725.6

Therefore he makes a payment of $100726.5 in 10 years as monthly instalments.

In addition to the 120th monthly payment he must have paid an amount equivalent to the present worth of the remaining 240 instalments.

PW = 839.38 * (P/A, .5%, 240) = 839.38 *139.58 = $117160.66

Therefore, in addition to the 120th monthly payment of $839.38, he must have paid an amount of $117160.66 to pay off the loan.