Multiple Choice
Approximately what annual interest rate, compounded annually, is needed to double an investment over eight years?
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10. Time Value of Money
Time Value of Money Equations
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What is the effective annual rate (EAR) of a 6\% annual percentage rate (APR) compounded daily? (Assume 365 days in a year.)
A
6.18\%
B
6.12\%
C
6.00\%
D
6.25\%
Verified step by step guidance1
Understand the concept: The Effective Annual Rate (EAR) accounts for compounding within a year, unlike the Annual Percentage Rate (APR), which does not. EAR is calculated using the formula: EAR = (1 + r/n)^(n) - 1, where r is the APR as a decimal, and n is the number of compounding periods per year.
Convert the APR to a decimal: Since the APR is given as 6%, divide it by 100 to express it as a decimal. This gives r = 0.06.
Determine the number of compounding periods per year: Since the interest is compounded daily, there are 365 compounding periods in a year. Thus, n = 365.
Substitute the values into the EAR formula: Replace r with 0.06 and n with 365 in the formula EAR = (1 + r/n)^(n) - 1. The formula becomes EAR = (1 + 0.06/365)^(365) - 1.
Simplify the expression: Calculate the value inside the parentheses (1 + 0.06/365), raise it to the power of 365, and subtract 1 to find the EAR. This will give the effective annual rate.
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