Question

You borrowed $220,000 for 30 years to buy a house. The mortgage, which has constant monthly payments and is fully amortizing, has an interest rate of 4.75% per year. What is the amount of interest you pay in the third year?

Question 2 options:

	1) $9,941
	2) $10,107
	3) $9,972
	4) $10,088
	5) $10,039

Answer 1

Loan Amount = PV = $220,000

n = 30 * 12 = 360 months

r = monthly interest rate = 4.75%/12 = 0.395833333%

Monthly loan payment = [r*PV] / [1 - (1+r)^-n]

= [0.395833333% * $220,000] / [1 - (1+0.395833333%)^-360]

= $870.833333 / 0.758813772

= $1,147.62457

Monthly loan payment is $1,147.62

x1 = 2*12 = 24 months

x2 = 3*12 = 36 months

Loan balance at the end of 2nd year = P * [1 - (1+r)^-(n-x1)] / r

= $1,147.62 * [1 - (1+0.395833333%)^-(360-24)] / 0.395833333%

= $1,147.62 * 0.734827181 / 0.00395833333

= $213,044.809

= $213,044.81

Loan balance at the end of 3rd year = P * [1 - (1+r)^-(n-x1)] / r

= $1,147.62 * [1 - (1+0.395833333%)^-(360-36)] / 0.395833333%

= $1,147.62 * 0.721953614 / 0.00395833333

= $209,246.78

Total amount paid in 3rd year = 12 * $1,147.62 = $13,771.44

Principal reduction in year 3 = loan balance at the end of year 2 - loan balance at the end of year 3

= $213,044.81 - $209,246.78

= $3,798.03

Interest paid in year 3 = Total amount paid in year 3 - principal reduction in year 3

= $13,771.44 - $3,798.03

= $9,973.41

Therefore, interest paid in year 3 is $9,973

Option 3 is correct