Which equation best represents the future value of a single sum after \(n\) periods, assuming no compounding interest (i.e., using simple interest)?

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

Answer: (B)

Verified step by step guidance

1. Understand the problem: The question is asking for the correct formula to calculate the future value (FV) of a single sum after \(n\) periods, assuming simple interest. Simple interest means that interest is calculated only on the principal amount (PV) and does not compound over time.
2. Recall the formula for simple interest: The future value (FV) under simple interest is calculated as \(FV = PV + (PV \times r \times n)\), where \(r\) is the interest rate per period, and \(n\) is the number of periods.
3. Simplify the formula: Factor out \(PV\) from the equation \(FV = PV + (PV \times r \times n)\) to get \(FV = PV \times (1 + r \times n)\). This is the formula for the future value under simple interest.
4. Compare the given options: The correct formula for simple interest is \(FV = PV \times (1 + r \times n)\). This matches one of the provided options.
5. Eliminate incorrect options: The other formulas provided either involve compounding interest (e.g., \(FV = PV \times (1 + r)^n\)) or are mathematically incorrect for simple interest (e.g., \(FV = PV \times (1 - r \times n)\) or \(FV = PV \div (1 + r \times n)\)).