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Multiple Choice
Given a loan with a nominal (stated) annual interest rate compounded quarterly, which of the following best describes how to calculate the Annual Percentage Rate (APR)?
A
Divide the quarterly rate by 4.
B
Add 4% to the quarterly rate.
C
Raise the quarterly rate to the 4th power.
D
Multiply the quarterly rate by 4.
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Verified step by step guidance
1
Understand the concept of Annual Percentage Rate (APR): APR represents the annualized interest rate, taking into account the nominal interest rate and the compounding frequency. It is calculated by multiplying the periodic interest rate by the number of compounding periods in a year.
Identify the periodic interest rate: Since the nominal annual interest rate is compounded quarterly, the quarterly interest rate is obtained by dividing the nominal annual interest rate by 4 (the number of quarters in a year).
Determine the number of compounding periods in a year: For quarterly compounding, there are 4 compounding periods in a year.
Calculate the APR: Multiply the quarterly interest rate by 4 (the number of compounding periods in a year). This step annualizes the quarterly rate to reflect the APR.
Verify the calculation: Ensure that the APR calculation aligns with the definition and formula for APR, which is the periodic rate multiplied by the number of compounding periods in a year.