Multiple Choice
Suppose you deposit \$5,000 into a savings account that earns 6\% annual interest, compounded annually. What is the total balance in the account after 40 years?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
If an account compounds interest monthly at a nominal rate of 2.5\% per year, what is the effective annual rate (EAR) for the account?
A
2.53\%
B
2.42\%
C
2.50\%
D
2.60\%
Verified step by step guidance1
Step 1: Understand the concept of Effective Annual Rate (EAR). EAR accounts for the effect of compounding within a year and 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.
Step 2: Identify the given values from the problem. The nominal annual interest rate (r) is 2.5% or 0.025 in decimal form, and the account compounds interest monthly, so the number of compounding periods per year (n) is 12.
Step 3: Substitute the values into the EAR formula. Using MathML, the formula becomes:
Step 4: Simplify the expression inside the parentheses first. Divide the nominal rate (0.025) by the number of compounding periods (12) to find the monthly interest rate.
Step 5: Calculate the EAR by raising the simplified value to the power of 12 (the number of compounding periods per year) and subtracting 1. This will give the effective annual rate, which can then be compared to the provided answer choices.
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