A $120,000 mortgage is amortized over 25 years. Interest is 7.5% compounded semi-annually for a 5-year term with monthly payments. At the end of the fifth year, the mortgage is renewed for a four year term at a rate of 7.0% compounded semi-annually. Determine the monthly payments of throughout the four year term.

Question

Quizplus · Accepted Answer

To find the monthly payments for the four year term, we need to use the formula for mortgage payments:

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

where:
P = monthly payment
PV = present value of the mortgage
r = interest rate per period
n = total number of periods

First, we need to find the present value of the mortgage at the end of the fifth year, which can be done using the formula:

PV = FV / (1 + r/2)^2n

where:
FV = future value of the mortgage
r = interest rate per period
n = number of periods

We know that the future value of the mortgage at the end of the fifth year is the remaining balance after 60 months of payments, which can be calculated using the PMT function in Excel or a financial calculator:

FV = -PMT(7.5%/12, 60, 120000) * (1 + 7.5%/2)^10
FV = $89,114.48

Plugging in these values into the formula, we get:

PV = 89114.48 / (1 + 7.0%/2)^2*4
PV = $76,370.95

Now we can plug in all the values into the mortgage payments formula:

P = (76370.95 * 7.0%/2) / (1 - (1 + 7.0%/2)^(-2*4*12))
P = $845.66

Therefore, the monthly payments throughout the four year term are $845.66. Choice C is the correct answer.

A $120,000 Mortgage Is Amortized Over 25 Years