Multiple Choice
Which of the following is typically involved in future value calculations in the context of the time value of money?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
Which of the following formulas correctly represents the future value of an ordinary annuity with periodic deposits of \(P\), interest rate \(r\) per period, and \(n\) periods?
A
\(FV = P \times \dfrac{(1 + r)^n - 1}{r}\)
B
\(FV = P \times (1 + r)^n\)
C
\(FV = P \times n \times r\)
D
\(FV = P \times \dfrac{1 - (1 + r)^{-n}}{r}\)
Verified step by step guidance1
Step 1: Understand the concept of an ordinary annuity. An ordinary annuity involves periodic payments or deposits made at the end of each period, and the future value represents the accumulated amount after all payments and interest have been applied.
Step 2: Analyze the formula for the future value of an ordinary annuity. The correct formula is: FV = P × ( (1 + r)^n - 1 ) / r. This formula accounts for the compounding effect of interest over multiple periods.
Step 3: Compare the given formulas. The first formula matches the correct formula for the future value of an ordinary annuity, as it includes the periodic deposit amount (P), the interest rate per period (r), and the number of periods (n), along with the compounding effect.
Step 4: Evaluate why the other formulas are incorrect. For example: FV = P × (1 + r)^n represents the future value of a single lump sum, not an annuity. FV = P × n × r does not account for compounding interest. FV = P × (1 - (1 + r)^-n) / r represents the present value of an ordinary annuity, not the future value.
Step 5: Conclude that the correct formula for the future value of an ordinary annuity is FV = P × ( (1 + r)^n - 1 ) / r, as it properly incorporates periodic deposits, compounding interest, and the number of periods.
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