The Future Value Formula

The future value of an investment is how much it will be worth after earning interest for a given period of time. It answers one specific question: if you put money away today, what will it grow to?

The Formula

$$F = P(1 + r)^n$$

• \(F\) = future value
• \(P\) = principal (amount invested today)
• \(r\) = annual interest rate as a decimal (6% → 0.06)
• \(n\) = number of years

The formula is just repeated multiplication — each year, the balance is multiplied by \((1 + r)\). After \(n\) years that multiplication has happened \(n\) times, which is why \(n\) is the exponent.

Example 1

You invest $1,000 at 5% annual interest for 10 years.

$$F = 1000(1.05)^{10} = 1000 \times 1.6289 \approx $1,629$$

You earned $629 in interest without adding a single dollar.

Example 2

You invest $4,500 at 7% for 15 years.

$$F = 4500(1.07)^{15} = 4500 \times 2.7590 \approx $12,416$$

The balance grew to nearly three times the original deposit. This is the compounding effect — interest earned in early years itself earns interest in later years.

For a deeper look at how compounding frequency (monthly, daily, continuous) affects the result, see the Compound Interest lesson.

Future Value Calculator

Practice Problems

1. You invest $2,500 at 4% annual interest for 6 years. What is the future value? Show answer\(F = 2500(1.04)^6 = 2500 \times 1.2653 \approx $3,163\).

2. Which grows to more after 20 years: $1,000 at 6%, or $800 at 8%? Show answerAt 6%: \(1000(1.06)^{20} \approx $3,207\). At 8%: \(800(1.08)^{20} \approx $3,732\). The lower principal at higher rate wins over 20 years.

3. You want $10,000 in 5 years. If you can earn 5% annually, how much do you need to invest today? (Hint: solve for P.) Show answerRearrange: \(P = \frac{F}{(1+r)^n} = \frac{10000}{(1.05)^5} = \frac{10000}{1.2763} \approx $7,835\). This is the present value calculation.