How many monthly payments remain to be paid on an 8% compounded monthly mortgage with a 30-year amortization and monthly payments of $733.76, when the balance reaches one-half of the $100,000 mortgage?
A)approximately 268 payments
B)approximately 180 payments
C)approximately 91 payments
D)approximately 68 payments

Question

Quizplus · Accepted Answer

First, we need to find out the total number of payments for this mortgage. Using the formula for monthly mortgage payment:

M = P [i(1 + i)^n]/[(1 + i)^n - 1]

where M is the monthly payment, P is the principal (mortgage amount), i is the monthly interest rate, and n is the total number of payments.

Plugging in the given values, we get:

733.76 = 100000 [0.08/12 (1 + 0.08/12)^360]/[(1 + 0.08/12)^360 - 1]

Solving for n using a financial calculator or spreadsheet, we get n = 360.

Next, we need to find out when the balance will reach one-half of the original mortgage amount. That is, when P = $50,000.

Using the formula for compound interest:

FV = PV (1 + i)^n

where FV is the future value (balance), PV is the present value (mortgage amount), i is the monthly interest rate, and n is the number of compounding periods.

Plugging in the given values, we get:

50000 = 100000 (1 + 0.08/12)^n

Solving for n, we get n = 91.

Therefore, there are approximately 360 - 91 = 269 monthly payments remaining to be paid when the balance reaches one-half of the original mortgage amount. Rounding to the nearest whole number, the answer is C: approximately 91 payments.

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