Multiple Choice
What is the present value of a $775 annuity payment received at the end of each year for 6 years, if the interest rate is 11\% per year? (Assume ordinary annuity)
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10. Time Value of Money
Time Value of Money Equations
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
What is the effective annual rate (EAR) if the nominal annual interest rate is 8.25\% compounded quarterly?
A
8.49\%
B
8.25\%
C
8.50\%
D
8.33\%
Verified step by step guidance1
Understand the concept of Effective Annual Rate (EAR): EAR is the actual interest rate earned or paid over a year, taking into account the effect of compounding. It 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.
Identify the given values: The nominal annual interest rate (r) is 8.25% or 0.0825 in decimal form, and the compounding frequency (n) is quarterly, which means there are 4 compounding periods per year.
Substitute the values into the formula: EAR = (1 + 0.0825/4)^4 - 1. Here, divide the nominal annual interest rate by the number of compounding periods to find the periodic interest rate.
Calculate the base of the exponent: Add 1 to the periodic interest rate (0.0825/4). This gives the base for the exponent in the formula.
Raise the base to the power of the number of compounding periods (4), then subtract 1 to find the EAR. This step completes the calculation for the effective annual rate.
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