Multiple Choice
What is the present value of \$500.00 to be received in two years if the annual interest rate is 5\% compounded annually?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
What is the effective annual rate (EAR) if the nominal annual interest rate is 14.9\% compounded quarterly?
A
16.02\%
B
14.90\%
C
15.44\%
D
15.81\%
Verified step by step guidance1
Understand the concept of Effective Annual Rate (EAR): EAR is the actual interest rate earned or paid over a year, taking into account the effect of compounding. It is calculated using the formula: EAR = (1 + r/n)^n - 1, where r is the nominal annual interest rate, and n is the number of compounding periods per year.
Identify the given values: The nominal annual interest rate (r) is 14.9% or 0.149 in decimal form, and the compounding frequency (n) is quarterly, meaning there are 4 compounding periods per year.
Substitute the values into the EAR formula: EAR = (1 + 0.149/4)^4 - 1. Break this down into smaller steps: first, divide the nominal rate by the number of compounding periods (0.149/4), then add 1 to the result.
Raise the result to the power of the number of compounding periods (4). This step accounts for the effect of compounding over the year.
Subtract 1 from the result to find the Effective Annual Rate (EAR). This final step gives the actual annual interest rate after considering compounding.
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