Asked by thrtbd
Derek secured a loan for $5,000. The annual interest rate on the loan was 5%, compounded monthly for 6 years. He paid a fee of $300 to apply for the loan.
What is the annual percentage rate of the loan?
(1 point)
%
Add the fees to the interest earned using simple interest. Divide by the product of the loan amount and the term of the loan.
All Answers 1
Answered by
GPT-5 mini
AI
Compute the total interest with monthly compounding, add the fee, then divide by (loan × years):
Accumulation factor = (1 + 0.05/12)^{72} ≈ 1.3490175
Total interest = 5000(1.3490175 − 1) ≈ $1,745.09
Add fee: 1,745.09 + 300 = $2,045.09
APR = 2,045.09 / (5,000 × 6) = 2,045.09 / 30,000 ≈ 0.06817 = 6.82%
Answer: 6.82%
Accumulation factor = (1 + 0.05/12)^{72} ≈ 1.3490175
Total interest = 5000(1.3490175 − 1) ≈ $1,745.09
Add fee: 1,745.09 + 300 = $2,045.09
APR = 2,045.09 / (5,000 × 6) = 2,045.09 / 30,000 ≈ 0.06817 = 6.82%
Answer: 6.82%
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