Last updated: 2026-05-13

Future value defined

Future value is the amount a sum of money will grow to at a given interest rate over a specified period, assuming compound interest. A single investment of $10,000 at 7 % per year grows to roughly $76,000 after 30 years, with no further contributions, because each period's interest is added to the principal and earns interest in turn.

The formula

The future value of a lump-sum investment is:

where $PV$ is the initial investment (present value), $r$ is the annual interest rate expressed as a decimal, $m$ is the number of compounding periods per year, and $n$ is the number of years.

When compounding occurs annually (one period per year), this simplifies to:

Worked example

For a principal of $10,000 at an annual rate of 7 %, compounded annually, over 30 years, the future value is:

The starting principal grows to about $76,000, of which roughly $66,000 is interest. The factor $(1 + r)^n$ — here about 7.6 — is the multiple by which the principal grows; it depends only on the rate and the horizon, not on the amount invested.

Compounding frequency

At a 7 % stated rate, the effective annual rate depends on how often interest is compounded:

On a $10,000 investment over 30 years, the difference between annual and monthly compounding is roughly $5,000 — meaningful, but still smaller than the effect of the rate or the horizon. The rate itself and the time invested move the result more than the compounding interval does.

Effect of the time horizon

Because the horizon sits in the exponent, lengthening it has an outsized effect on the result. Consider two lump sums of $10,000, each invested at 7 % per year:

• A sum invested for 40 years grows to about $150,000.
• A sum invested for 30 years grows to about $76,000.

The additional ten years account for nearly $74,000 — about 7.4 times the original principal — with no additional contribution. A longer horizon typically affects the ending balance more than a larger starting amount invested later.

The Rule of 72

The Rule of 72 estimates the doubling time of an investment: dividing 72 by the annual interest rate gives the approximate number of years to double — $\text{Doubling time} \approx 72 / r\%$.

At 6 %, money doubles in about 12 years. At 9 %, about 8 years. The approximation is accurate to within a year for rates between 2 % and 20 %. See the Rule of 72 Calculator for a precise comparison.

Assumptions and limits

The future value formula assumes:

1. A fixed nominal rate. Real investment returns fluctuate year to year. A 7 % long-run average may include years of −20 % and +30 %.
2. No taxes or fees. Management fees reduce the effective return. At 0.5 % annual fees, the effective rate on a 7 % gross return drops to 6.5 % — which over 30 years on $10,000 is roughly $10,000 less.
3. No inflation adjustment. The future value is nominal. To express it in today's purchasing power, use an inflation calculator with the same horizon.
4. A single lump sum. For periodic contributions on top of the principal, the Compound Interest Calculator handles regular deposits.

Practical applications

• Retirement planning. Estimate what a lump-sum rollover or existing balance will grow to by retirement.
• Education savings. Project how much a one-time contribution will be worth when tuition is due.
• Comparing offers. Two savings accounts with different rates and compounding frequencies can be compared directly using this calculator.
• Reverse calculation. To find what a future sum is worth today, use the Present Value Calculator.