Loan amount = $10,000
Monthly payments = $258.50
Time of loan contract = 5 years
True annual interest rate (to the nearest tenth) =
21.7%
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To find the true annual interest rate, we need to use the formula for calculating the annual interest rate:
True Annual Interest Rate = (Total Interest / Loan Amount) * (1 / Number of Years) * 100
First, let's calculate the total interest paid over the duration of the loan:
Total Interest = (Monthly Payment * Number of Payments) - Loan Amount
Number of Payments = (Number of Years) * (Number of Payments per Year)
In this case:
Loan Amount = $10,000
Monthly Payment = $258.50
Time of Loan Contract = 5 years
Number of Payments per Year: Since we know the loan term is 5 years, and a year has 12 months, the number of payments per year would be 12.
Number of Payments = (Number of Years) * (Number of Payments per Year) = 5 * 12 = 60
Total Interest = (Monthly Payment * Number of Payments) - Loan Amount = ($258.50 * 60) - $10,000 = $15,510 - $10,000 = $5,510
Now, we can calculate the true annual interest rate:
True Annual Interest Rate = (Total Interest / Loan Amount) * (1 / Number of Years) * 100
True Annual Interest Rate = ($5,510 / $10,000) * (1 / 5) * 100 ≈ 0.551 * 0.2 * 100 ≈ 11.02
Therefore, the true annual interest rate (to the nearest tenth) is approximately 11.0%.