Gladys Turner borrowed $12,000 from the bank using a 10.19 percent "add-on", one-year installment loan, payable in four equal quarterly payments.What is the effective annual rate of interest?
A) 9.50%
B) 10.19%
C) 15.99%
D) 16.98%
E) 20.38%

Question

Quizplus · Accepted Answer

Using the add-on method, the total amount that Gladys would have to pay back is:

Total amount = (Loan amount) + (Interest)
Total amount = $12,000 + ($12,000 x 10.19% x 1)
Total amount = $12,000 + $1,222.80
Total amount = $13,222.80

Since the loan is payable in four equal quarterly payments, each payment would be:

Payment = (Total amount) / (Number of payments)
Payment = $13,222.80 / 4
Payment = $3,305.70

To calculate the effective annual rate of interest, we can use the following formula:

Effective annual rate = ((1 + (periodic rate))^n - 1) x 100%

Where:
- Periodic rate = the interest rate per payment period (in this case, per quarter)
- n = the number of payment periods in a year

For this loan, the periodic rate can be calculated as:

Periodic rate = (Add-on rate) / (Number of payments)
Periodic rate = 10.19% / 4
Periodic rate = 2.5475%

Using this periodic rate and the number of payment periods in a year (4), we can calculate the effective annual rate as:

Effective annual rate = ((1 + 2.5475%)^4 - 1) x 100%
Effective annual rate = (1.025475^4 - 1) x 100%
Effective annual rate = 16.98%

Therefore, the answer is D - 16.98%.

Gladys Turner Borrowed $12,000 from the Bank Using a 10