Multiple Choice
What is the present value of a \$775 annuity payment received at the end of each year for 6 years, if the interest rate is 11\% per year? (Assume ordinary annuity)
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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 8.25\% compounded quarterly?
A
8.49\%
B
8.25\%
C
8.50\%
D
8.33\%
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 8.25% or 0.0825 in decimal form, and the compounding frequency (n) is quarterly, which means there are 4 compounding periods per year.
Substitute the values into the formula: EAR = (1 + 0.0825/4)^4 - 1. Here, divide the nominal annual interest rate by the number of compounding periods to find the periodic interest rate.
Calculate the base of the exponent: Add 1 to the periodic interest rate (0.0825/4). This gives the base for the exponent in the formula.
Raise the base to the power of the number of compounding periods (4), then subtract 1 to find the EAR. This step completes the calculation for the effective annual rate.
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