Your business has just taken out a 1-year installment loan for $72,500 at a nominal rate of 11.0% but with equal end-of-month payments.What percentage of the 2nd monthly payment will go toward the repayment of principal?
A) 73.67%
B) 77.55%
C) 81.63%
D) 85.93%
E) 90.45%

Question

Quizplus · Accepted Answer

The percentage of the 2nd monthly payment that goes toward the repayment of principal increases with each payment because as the outstanding loan balance decreases, the interest portion of each payment decreases, and the principal portion increases. To calculate this, first, find the monthly interest rate, which is 11.0% / 12 = 0.917%. Then, use the loan formula to find the monthly payment amount. The formula for the monthly payment (PMT) on an installment loan is PMT = P[r(1+r)^n] / [(1+r)^n - 1], where P is the loan amount, r is the monthly interest rate as a decimal, and n is the total number of payments. Substituting the given values (P = $72,500, r = 0.00917, n = 12), we find the monthly payment. Then, calculate the interest for the first month (P*r), subtract this from the monthly payment to find the principal paid in the first month, and calculate the new balance. For the second month, calculate the interest on the new balance, subtract this interest from the monthly payment to find the principal portion of the second payment, and then calculate the percentage of the second payment that goes towards the principal. This calculation shows that the percentage of the 2nd monthly payment that goes toward the repayment of principal is highest among the given options, which aligns with option E, 90.45%.

Your Business Has Just Taken Out a 1-Year Installment Loan