Join thousands of students who trust us to help them ace their exams!Watch the first video
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 guidance
1
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.