Your current $95,000 mortgage calls for monthly payments over 30 years at an annual rate interest rate of 6 percent.If you pay an additional $50 each month beginning with the first payment,how soon do you pay off your mortgage?

Question

Quizplus · Accepted Answer

To solve this problem we will use the formula for the present value of an annuity:

PV = A * [(1 - (1 + r)^(-n)) / r]

Where:
PV = present value or the initial loan amount ($95,000)
A = monthly payment ($572.90)
r = monthly interest rate (6% / 12 = 0.005)
n = total number of payments (30 years * 12 = 360 months)

Using this formula, we can find the present value of the loan:

PV = 572.90 * [(1 - (1 + 0.005)^(-360)) / 0.005] = $95,000

Now, if we add $50 to the monthly payment, the new monthly payment will be $622.90. We want to find out how long it will take to pay off the loan with this higher payment amount. We can use the same formula:

PV = 622.90 * [(1 - (1 + 0.005)^(-n)) / 0.005]

We want to solve for n, so we'll need to use a numerical method like trial and error or a financial calculator. Using trial and error, we find that the answer is approximately 291.78 months, or about 24 years and 3 months. Therefore, the best choice is C.

Your Current $95,000 Mortgage Calls for Monthly Payments Over 30