Question

You just entered into a $150,000 30-year home mortgage at an annual interest rate of 4.25% making monthly payments of $737.91. Suppose you add an additional payment of $295.97 each month to the $737.91 house payment making your total monthly payments equal to $1,033.88. This extra amount is applied against the principal of the original loan. How long will it take you to pay off your loan of $150,000? Use a calculator to determine your answer.

a. It will take about 186 months.

b. It will take about 206 months.

c. It will take about 216 months.

d. It will take about 265 months.

Answer 1

Given ,

Loan Amount = $150,000

Interest rate = 4.25% p.a. or 0.354% per month

Loan repayment revised = $1,033.88

Repayment term = ?

Now using formula Present value of annuity

PVA = PMT x (1-(1+r)^-n)/r

Putting values

150000 = 1033.88 x (1-(1+.00354)^-n)/0.00354

150000 x 0.00354/1033.88 = 1-(1.003542)^-n

1.00354^-n = 1-0.5136

Taking Ln both sides,

-n x Ln(1.00354) = Ln(.4864)

-n = Ln(.4864)/Ln(1.00354) => -0.7207/0.0035

N = 206 Option B