Multiple Choice
The formula PV = FV (1 + r)n is best used for:
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
What is the effective annual rate (EAR) for an investment that pays 10\% interest compounded annually?
A
9.5\%
B
9.09\%
C
10.25\%
D
10\%
Verified step by step guidance1
Understand the concept of Effective Annual Rate (EAR): EAR is the actual interest rate earned or paid on an investment or loan after accounting for compounding over a year. It is calculated using the formula: EAR = (1 + r/n)^n - 1, where r is the nominal interest rate and n is the number of compounding periods per year.
Identify the given values: In this problem, the nominal interest rate (r) is 10% or 0.10, and the compounding frequency (n) is 1 since the interest is compounded annually.
Substitute the values into the EAR formula: EAR = (1 + 0.10/1)^1 - 1. This simplifies to EAR = (1 + 0.10)^1 - 1.
Simplify the expression inside the parentheses: Add 1 to 0.10, resulting in EAR = (1.10)^1 - 1.
Interpret the result: Since the interest is compounded annually, the EAR is equal to the nominal interest rate, which is 10%. This confirms the correct answer provided in the problem.
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