Multiple Choice
Which of the following is the formula for the future value of an ordinary annuity, where \(PMT\) is the periodic payment, \(r\) is the interest rate per period, and \(n\) is the number of periods?
10. Time Value of Money
Time Value of Money Equations
Multiple Choice
Which of the following best describes the formula \( EAR = (1 + \frac{rate}{m})^m - 1 \)?
A
It calculates the effective annual rate (EAR) given a nominal rate compounded m times per year.
B
It determines the future value of an ordinary annuity.
C
It computes the simple interest earned over one year.
D
It calculates the present value of a future sum using continuous compounding.
Verified step by step guidance1
Understand the formula: The formula \( EAR = (1 + \frac{rate}{m})^m - 1 \) is used to calculate the Effective Annual Rate (EAR), which accounts for the effects of compounding within a year.
Break down the components: \( rate \) represents the nominal interest rate, and \( m \) is the number of compounding periods per year. The formula adjusts the nominal rate to reflect the impact of compounding.
Interpret the formula: The term \( \frac{rate}{m} \) divides the nominal rate by the number of compounding periods, giving the periodic rate. Raising \( (1 + \frac{rate}{m}) \) to the power of \( m \) accounts for compounding over all periods in the year.
Subtract 1: The subtraction of 1 at the end of the formula removes the principal amount, leaving only the effective annual rate (EAR), which represents the true annual return on investment after compounding.
Clarify the purpose: This formula specifically calculates the EAR, which is the annualized interest rate that includes the effects of compounding, making it distinct from simple interest or other financial calculations like future value or present value.
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