Which of the following formulas represents a present value factor?

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

Answer: (D)

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 stream of cash flows, given a specified rate of return (r). The present value factor is used to discount future values to their present value.
2. Review the formula for present value: The formula for calculating present value is \(PV = \dfrac{FV}{(1 + r)^n}\), where FV is the future value, r is the interest rate, and n is the number of periods. This formula shows how future values are discounted to present values.
3. Identify the present value factor: The present value factor is the portion of the formula that discounts the future value. It is represented as \(\dfrac{1}{(1 + r)^n}\). This factor is multiplied by the future value to calculate the present value.
4. Compare the given formulas: Analyze each formula provided in the problem and determine which one matches the present value factor. The correct formula is \(\dfrac{1}{(1 + r)^n}\), as it represents the discounting mechanism for future values.
5. Conclude the reasoning: The formula \(\dfrac{1}{(1 + r)^n}\) is the correct representation of the present value factor because it discounts future values to their present worth based on the interest rate and number of periods.