Multiple Choice
What is the present value (PV) of an annuity due consisting of 5 payments of \$2,500 each, with an interest rate of 5.5% per period?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
In calculating the yield of an investment, what is the Effective Annual Rate (EAR) equivalent to?
A
The present value of future cash flows
B
The annual interest rate that accounts for compounding within the year
C
The simple interest rate applied only once per year
D
The stated nominal interest rate without compounding
Verified step by step guidance1
Understand the concept of Effective Annual Rate (EAR): EAR is the annual interest rate that accounts for the effects of compounding within the year, making it a more accurate measure of the true cost or return of an investment compared to nominal rates.
Identify the formula for EAR: The formula is EAR = (1 + i/n)^n - 1, where 'i' is the nominal interest rate, and 'n' is the number of compounding periods per year.
Break down the formula: (1 + i/n) represents the interest rate per compounding period, raised to the power of 'n' to account for all compounding periods in a year. Subtracting 1 adjusts the result to reflect the effective annual rate.
Compare EAR to other rates: Unlike the nominal interest rate, which does not account for compounding, EAR provides a more realistic measure of the investment's yield when compounding occurs multiple times within a year.
Apply the formula to calculate EAR: Substitute the given nominal interest rate and the number of compounding periods into the formula to determine the EAR. This step requires performing the mathematical operations outlined in the formula.
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