Which equation best represents the calculation of future value (\(FV\)) using simple interest?

• A. \(FV = PV \times (1 + r)^t\)
• B. \(FV = PV \times (1 + rt)\)
• C. \(FV = PV \div (1 + rt)\)
• D. \(FV = PV + (PV \times r \times t^2)\)

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the concept of simple interest. Simple interest is calculated on the principal amount ( MathML: PV ) over a period of time ( MathML: t ) at a fixed interest rate ( MathML: r ). The formula for simple interest is MathML: Interest = PV × r × t.
2. Step 2: Recognize that the future value ( MathML: FV ) is the sum of the principal amount ( MathML: PV ) and the interest earned. Therefore, the formula for future value using simple interest is MathML: FV = PV + (PV × r × t).
3. Step 3: Simplify the formula for future value. Factor out MathML: PV from the equation: MathML: FV = PV × (1 + r × t).
4. Step 4: Compare the simplified formula ( MathML: FV = PV × (1 + r × t) ) with the options provided in the problem. This matches the correct answer.
5. Step 5: Note that other options provided in the problem do not align with the principles of simple interest. For example, MathML: FV = PV × (1 + r)^t represents compound interest, and MathML: FV = PV ÷ (1 + r × t) is not a valid formula for future value.