Which of the following represents the basic present value equation?

• A. \(PV = FV - (r \times n)\)
• B. \(PV = \dfrac{FV}{(1 + r)^n}\)
• C. \(PV = FV \times (1 + r)^n\)
• D. \(PV = FV \div r\)

Answer: (B)

Verified step by step guidance

1. Understand the concept of present value (PV): Present value is the current worth of a future sum of money or cash flow, given a specific rate of return (r) and time period (n). It accounts for the time value of money.
2. Identify the correct formula for present value: The basic present value equation is derived from the principle that future value (FV) is discounted back to the present using the formula \(PV = \dfrac{FV}{(1 + r)^n}\). This formula accounts for the compounding effect of the interest rate over time.
3. Break down the formula: In the equation \(PV = \dfrac{FV}{(1 + r)^n}\), FV represents the future value, r is the interest rate (expressed as a decimal), and n is the number of compounding periods.
4. Compare the given options: Analyze each option provided in the problem. The correct formula is \(PV = \dfrac{FV}{(1 + r)^n}\), as it properly discounts the future value to the present value using the compounding factor \((1 + r)^n\). The other options do not correctly represent the relationship between PV, FV, r, and n.
5. Conclude the reasoning: The correct answer is \(PV = \dfrac{FV}{(1 + r)^n}\) because it aligns with the fundamental principles of the time value of money and accurately calculates the present value of a future sum.