John House has taken a 20-year, $250,000 mortgage on his house at an interest rate of 6% per year. What is the value of the mortgage after the payment of the fifth annual installment?
A) $128,958.41
B) $211,689.53
C) $141,019.50
D) None of the above

Question

Quizplus · Accepted Answer

To calculate the value of the mortgage after the payment of the fifth annual installment, we need to use the formula for mortgage balance after n payments:

M = P * ((1 + r)^n - 1) / r

where M is the mortgage balance, P is the amount borrowed, r is the interest rate per year, and n is the number of payments made.

Since John has taken a 20-year mortgage and has made five annual payments, the number of payments remaining is 20 - 5 = 15.

Plugging in the values, we get:

M = $250,000 * ((1 + 0.06)^15 - 1) / 0.06
M = $211,689.53

Therefore, the answer is B, $211,689.53.

John House Has Taken a 20-Year, $250,000 Mortgage on His