Future Value
Future worth of a present sum.
Formula
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Example
$500 growing at 6% for 4 years becomes 500·1.06⁴ ≈ $631.24.
How it works
This formula tells you how a single amount of money grows when it earns the same rate of return each period. The idea is compound growth: after each period, the new total becomes the base for the next period, so the money grows on both the original amount and the accumulated growth. The exponent n counts how many times that growth is applied.
When to use it
Use it when you know a present amount and want to predict its value after a fixed number of compounding periods at a constant rate. It is common in savings, investments, loans, and any situation with steady percentage growth per period.
Worked example, step by step
Suppose you invest $1,200 at 4% per year for 3 years. Use the formula: FV = PV(1 + r)^n Substitute the values: FV = 1200(1 + 0.04)^3 Simplify inside the brackets: FV = 1200(1.04)^3 Calculate the power: FV = 1200(1.124864) Multiply: FV = 1349.8368 Final answer: FV ≈ $1,349.84
Common mistakes to avoid
- Using the rate as 4 instead of 0.04
- Adding the rate each year instead of compounding it
- Forgetting that n must match the number of compounding periods, not just calendar years
Did You Know?
A dollar today is worth more than a dollar tomorrow — the core idea behind the time value of money.
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