Question

Travis received a 25 year loan of $330,000 to purchase a house. The interest rate on the loan was 4.90% compounded monthly.

a. What is the size of the monthly loan payment? $ Round to the nearest cent
b. What is the principal balance of the loan at the end of 3 years? $ Round to the nearest cent
c. By how much will the amortization period shorten if Travis made an extra payment of $50,000 at the end of the year 3? years months Express the answer in years and months, rounded to the next month

Answer 1

a. Monthly loan payment:

$330,000 loan amount

25 year loan term

4.90% annual interest rate

Compounded monthly

Monthly interest rate = 0.0475% (4.90% / 12 months)

Monthly payment = $330,000 * (0.0475% * (1 - (1 / (1 + 0.0475%)^(25 * 12)))) / (1 - (1 / (1 + 0.0475%)^(25 * 12))) = $1,711.19 (rounded to the nearest cent)

b. Principal balance after 3 years:

Year 1: $330,000 * (1 - (1 / (1 + 0.0475%)^12)) = $309,644 (rounded to the nearest cent)

Year 2: $309,644 * (1 - (1 / (1 + 0.0475%)^12)) = $287,020 (rounded to the nearest cent)

Year 3: $287,020 * (1 - (1 - (1 / (1 + 0.0475%)^12))) = $264,148 (rounded to the nearest cent)

c. Extra payment of $50,000 at year 3:

Remaining principal balance after extra payment = $264,148 - $50,000 = $214,148

Time needed to pay off $214,148 at monthly payment of $1,711.19 =

$214,148 / $1,711.19 per month = 12 years (rounded up)

So amortization period shortened by 3 years.

In years and months:

3 years