Coverall Carpets Inc. is planning to borrow $12,000 from the bank. The bank offers the choice of a 12 percent discount interest loan or a 10.19 percent add-on, one-year installment loan, payable in 4 equal quarterly payments. What is the approximate (nominal) rate of interest on the 10.19 percent add-on loan?

Question

Quizplus · Accepted Answer

To determine the approximate nominal rate of interest on the 10.19 percent add-on loan, we need to understand how the add-on interest works and then calculate the nominal annual interest rate based on the quarterly payments.
An add-on interest loan means that the interest is calculated on the original principal at the beginning and then added to the principal. The borrower then repays the sum of the principal and the added interest in equal installments over the loan period.
For Coverall Carpets Inc., the loan amount is $12,000, and the add-on interest rate is 10.19 percent for a one-year loan. The interest amount for the year would be:
Interest = Principal × Add-on Interest Rate
Interest = $12,000 × 0.1019
Interest = $1,222.80
The total amount to be repaid is the principal plus the interest:
Total Repayment = Principal + Interest
Total Repayment = $12,000 + $1,222.80
Total Repayment = $13,222.80
This total repayment is to be made in 4 equal quarterly payments:
Quarterly Payment = Total Repayment / 4
Quarterly Payment = $13,222.80 / 4
Quarterly Payment = $3,305.70
Now, to find the nominal annual interest rate, we need to consider that the borrower is not actually using the full $12,000 throughout the entire year because they are making quarterly payments. However, the interest is calculated as if they did. To find the nominal rate, we need to compare the interest paid to the average balance over the year.
The average balance over the year can be approximated by taking the midpoint of the loan balance since the payments are made in equal installments. The midpoint between the full amount and zero is $6,000 (half of $12,000).
Nominal Annual Interest Rate = (Total Interest / Average Balance) × Number of Periods per Year
Nominal Annual Interest Rate = ($1,222.80 / $6,000) × 4
Nominal Annual Interest Rate = 0.2038 or 20.38%
Therefore, the approximate nominal rate of interest on the 10.19 percent add-on loan is 20.38%.
The correct answer is:
d. 20.38%