Noah paid off a loan with a simple interest rate of 9.7\% for 4 months. What was the annual percentage rate (APR) for the loan?

• A. 9.7\%
• B. 29.1\%
• C. 24.25\%
• D. 38.8\%

Answer: (B)

Verified step by step guidance

1. Understand the concept of APR (Annual Percentage Rate): APR represents the annualized interest rate, which includes the simple interest rate adjusted for the time period of the loan.
2. Identify the given values: The simple interest rate is 9.7%, and the loan duration is 4 months. Convert the loan duration into a fraction of a year. Since there are 12 months in a year, 4 months is equivalent to 4/12 or 1/3 of a year.
3. Calculate the annualized interest rate: Multiply the simple interest rate by the reciprocal of the fraction of the year. The formula is: APR = Simple Interest Rate × (12 / Loan Duration in Months). Using MathML, the formula is: $\mathrm{APR}=\mathrm{Simple\; Interest\; Rate}\times \frac{12}{\mathrm{Loan\; Duration\; in\; Months}}$
4. Substitute the values into the formula: Replace the simple interest rate with 9.7% and the loan duration with 4 months. The calculation becomes: APR = 9.7 × (12 / 4). Using MathML, the substitution is: $\mathrm{APR}=9.7\times \frac{12}{4}$
5. Interpret the result: The calculated APR represents the annualized interest rate for the loan. Compare the result to the provided answer choices to determine the correct option.