Given a present value (PV), an annual interest rate \(r\), and \(n\) years, what is the correct formula to calculate the future value (FV)?

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

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the concept of Future Value (FV). Future Value is the value of a current asset or amount of money at a specified date in the future, based on an assumed rate of growth or interest.
2. Step 2: Recall the formula for calculating Future Value (FV) using compound interest. The correct formula is FV = PV × (1 + r)^n, where PV is the present value, r is the annual interest rate, and n is the number of years.
3. Step 3: Analyze the given options. The correct formula should reflect the compounding effect of interest over time, which is represented by (1 + r)^n.
4. Step 4: Eliminate incorrect options. For example, FV = PV ÷ (1 + r)^n is incorrect because it represents a discounting formula for present value, not future value. Similarly, FV = PV × (1 - r)^n and FV = PV + (r × n) do not account for compounding interest.
5. Step 5: Confirm that FV = PV × (1 + r)^n is the correct formula for calculating Future Value, as it properly incorporates the compounding effect of interest over the specified number of years.