Multiple Choice
Which of the following equations correctly calculates the future value ($FV$) of a single sum invested today ($PV$) for $n$ periods at an annual interest rate $r$, with interest compounded once per period?
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10. Time Value of Money
Time Value of Money Equations
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What is the present value of a \$200 payment to be received in three years if the discount rate is 8\% per year, compounded annually?
A
\$147.20
B
\$160.00
C
\$180.00
D
\$158.73
Verified step by step guidance1
Step 1: Understand the concept of present value (PV). Present value is the current worth of a future sum of money, discounted at a specific interest rate. The formula for PV is: PV = FV / (1 + r)^n, where FV is the future value, r is the discount rate, and n is the number of periods.
Step 2: Identify the given values in the problem. Here, the future value (FV) is $200, the discount rate (r) is 8% or 0.08, and the number of periods (n) is 3 years.
Step 3: Substitute the given values into the present value formula. Using MathML, the formula becomes:
Step 4: Perform the calculation step-by-step. First, calculate (1 + r), which is (1 + 0.08) = 1.08. Then raise 1.08 to the power of 3 (n = 3). Finally, divide the future value ($200) by the result of 1.08^3.
Step 5: Interpret the result. The calculated present value represents the amount you would need to invest today at an 8% annual interest rate to receive $200 in three years. Compare the calculated value to the provided options to determine the correct answer.
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