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Multiple Choice
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\%
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.
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.
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:
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:
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.