Multiple Choice
Your credit card company charges you 1.15\% interest per month. What is the annual percentage rate (APR)?
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10. Time Value of Money
Time Value of Money Equations
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Given an effective annual rate (EAR) of 14% and semiannual compounding, what is the nominal annual interest rate (APR) compounded semiannually?
A
12.00%
B
14.00%
C
13.53%
D
7.00%
Verified step by step guidance1
Understand the relationship between the Effective Annual Rate (EAR) and the Nominal Annual Interest Rate (APR). The EAR accounts for compounding, while the APR is the nominal rate without compounding adjustments.
Use the formula to convert EAR to APR for semiannual compounding: \( EAR = \left(1 + \frac{APR}{n}\right)^n - 1 \), where \( n \) is the number of compounding periods per year. For semiannual compounding, \( n = 2 \).
Rearrange the formula to solve for APR: \( APR = n \times \left(\sqrt[n]{EAR + 1} - 1\right) \). Substitute \( EAR = 0.14 \) and \( n = 2 \) into the formula.
Calculate the intermediate step \( \sqrt[n]{EAR + 1} \), which is \( \sqrt[2]{0.14 + 1} \). This represents the semiannual compounding factor.
Multiply the result by \( n \) (which is 2) to find the nominal annual interest rate (APR) compounded semiannually.
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