On December 1, 2014, Crawley Corporation incurs a 15-year $600,000 mortgage liability in conjunction with the acquisition of an office building. This mortgage is payable in monthly installments of $7,200, which include interest computed at the rate of 12% per year. The first monthly payment is made on December 31, 2014. The portion of the second monthly payment made on January 31, 2015, which represents repayment of principal is:

Question

Quizplus · Accepted Answer

The amount of interest accrued on the first payment, made on December 31, 2014, can be calculated as:

Interest = P × r × t
Where:
P = Principal = $600,000
r = Monthly interest rate = Annual interest rate ÷ 12 = 12% ÷ 12 = 1%
t = Time = 1 month

Interest = $600,000 × 1% × 1 = $6,000

Therefore, the amount of the first payment that goes towards principal repayment is:

Principal = Payment - Interest = $7,200 - $6,000 = $1,200

Now, we need to calculate the remaining mortgage balance after the first payment. We can do this using the formula for the present value of an annuity:

PV = P × [((1 + r)^n - 1) ÷ (r × (1 + r)^n)]
Where:
PV = Present value of the mortgage
P = Payment amount = $7,200
r = Monthly interest rate = 1%
n = Total number of payments = 15 years × 12 months/year = 180

PV = $600,000 × [((1 + 1%)^180 - 1) ÷ (1% × (1 + 1%)^180)] = $498,703.46 (rounded)

Therefore, the amount of principal repayment included in the second payment, made on January 31, 2015, is:

Principal = Payment - Interest = $7,200 - ($498,703.46 × 1% ÷ 12) = $1,211.94 (rounded)

The correct answer is therefore B) $1,212.

On December 1, 2014, Crawley Corporation Incurs a 15-Year $600,000