Which formula correctly computes future value given present value and rate r over n years?

• A. Future value = Present value × (1 + r)^n
• B. Future value = Present value ÷ (1 + r)^n
• C. Future value = Present value × (1 - r)^n
• D. Future value = Present value × (1 + r)

Answer: (A)

Understanding how future value grows with time helps make sense of this formula. When you invest a present amount at a rate r each year, the value is multiplied by 1 + r at the end of every year. After one year you have PV × (1 + r). After two years you have PV × (1 + r) × (1 + r) = PV × (1 + r)², and so on. After n years, you’ve applied that growth n times, giving FV = PV × (1 + r)ⁿ. This captures the idea of compounding: earnings from previous years also earn interest in subsequent years.

The other forms don’t represent growth over multiple periods. Dividing by (1 + r)ⁿ discounts into the present value rather than projecting future value. Using (1 − r)ⁿ would imply a decrease in value each year, which isn’t the standard growth model for positive r. Using only (1 + r) would apply to a single period, not n years.