Buffon Electronics Company issues a $1,000,000, 10%, 20-year mortgage note on January 1. The terms provide for semiannual installment payments, exclusive of real estate taxes and insurance, of $58,276. After the first installment payment, the principal balance is
A) $1,000,000.
B) $983,034.
C) $991,724.
D) $779,125.

Question

Quizplus · Accepted Answer

First, we need to find out how many payments there will be over the course of the 20-year mortgage note, and we know that each payment will be $58,276.

There are 20 years in the mortgage, and since payments are made semiannually (twice per year), there will be 20 x 2 = 40 payments.

Next, we need to use the mortgage amortization formula to calculate the principal balance after the first payment.

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

Where PV is the beginning principal balance, PMT is the payment amount, r is the interest rate (as a decimal), n is the number of payments per year, and t is the total number of years.

Plugging in the values, we get:

PV = $58,276 x (1 - (1 + 0.10/2)^(-2x20)) / (0.10/2)
PV = $58,276 x (1 - (1.05)^(-40)) / 0.05
PV = $991,724.14

Therefore, the principal balance after the first installment payment is $991,724.14, which is choice C.

Buffon Electronics Company Issues a $1,000,000, 10%, 20-Year Mortgage Note