Question

You bought a house for $150,000 and put down 10% and got a mortgage at an interest rate of 4.35 % per year. You would pay it back by paying an equal amount at the end of each month for 15 years? (Show all work) How much is your loan amount? How much is your monthly loan payment? How much is your loan balance after 2 years? How much is your total interest payment by the end of year 3?

Answer 1

Answer a.

Cost of house = $150,000

Down payment = 10% * $150,000
Down payment = $15,000

Amount borrowed = $150,000 - $15,000
Amount borrowed = $135,000

Answer b.

Annual interest rate = 4.35%
Monthly interest rate = 0.3625%

Period = 15 years or 180 months

Let monthly payment be $x

$135,000 = $x/1.003625 + $x/1.003625^2 + … + $x/1.003625^179 + $x/1.003625^180
$135,000 = $x * (1 - (1/1.003625)^180) / 0.003625
$135,000 = $x * 132.039440
$x = $1,022.42

Monthly payment = $1,022.42

Answer c.

Remaining period = 13 years or 156 months

Loan outstanding after 2 years = $1,022.42/1.003625 + $1,022.42/1.003625^2 + … + $1,022.42/1.003625^155 + $1,022.42/1.003625^156
Loan outstanding after 2 years = $1,022.42 * (1 - (1/1.003625)^156) / 0.003625
Loan outstanding after 2 years = $1,022.42 * 118.991120
Loan outstanding after 2 years = $121,658.90

Answer d.

Remaining period = 12 years or 144 months

Loan outstanding after 3 years = $1,022.42/1.003625 + $1,022.42/1.003625^2 + … + $1,022.42/1.003625^143 + $1,022.42/1.003625^144
Loan outstanding after 3 years = $1,022.42 * (1 - (1/1.003625)^144) / 0.003625
Loan outstanding after 3 years = $1,022.42 * 112.029525
Loan outstanding after 3 years = $114,541.23

Loan repaid = $135,000 - $114,541.23
Loan repaid = $20,458.77

Total amount paid = 36 * $1,022.42
Total amount paid = $36,807.12

Interest paid = $36,807.12 - $20,458.77
Interest paid = $16,348.35