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Future Value Calculator: Growth of a Lump Sum
Enter an amount today, a yearly rate, the number of years and how often interest compounds. You get the future value, the growth earned and, if you add inflation, the value in today's money.
The future value formula
Future value (FV) is what an amount today will be worth after it earns interest for a set time. For periodic compounding the formula is FV = PV × (1 + r ÷ n)n × t, where PV is the present amount, r the annual rate as a decimal, n the number of compounding periods per year and t the time in years. For continuous compounding, the limit as n grows without bound, the formula becomes FV = PV × er × t, where e is about 2.71828.
The calculation shares its logic with the compound interest calculator, but this page focuses on a single lump sum with no further deposits, which keeps the formula visible.
How compounding frequency changes the answer
The more often interest is added, the more interest earns interest, though the effect has a ceiling. This table shows 1,000 at a 5% annual rate over 10 years.
| Compounding | Future value |
|---|---|
| Yearly | 1,628.89 |
| Monthly | 1,647.01 |
| Continuous | 1,648.72 |
Going from yearly to monthly adds about 18 on this amount, whereas going from monthly to continuous adds under 2. Time and rate drive the outcome far more than frequency.
Nominal and real future value
The headline figure is nominal: it counts units of currency, not what they buy. If prices rise, a larger number can still buy the same or less. The optional inflation input divides the future value by (1 + inflation)t to give the result in today's purchasing power. A rate of 7% with 3% inflation, for instance, gives a real growth rate of roughly 3.9% a year, not 4%, because the two effects compound together. Use the inflation calculator if you want to study price changes on their own.
Assumptions and when to use another tool
- The rate is constant and no money is added or taken out. For regular deposits use the annuity calculator or the compound interest calculator.
- Fees and taxes are ignored. Enter a rate net of both for a closer estimate.
- Negative rates are allowed, to model a loss, but a rate below minus 100% divided by the compounding count is rejected.
- To go backwards, from a future sum to its worth today, use the present value calculator.
Before relying on a figure, repeat the calculation with a rate one or two points lower, because the gap between the two answers shows how fragile the projection is. Long horizons magnify small differences in the rate, which is why a single number should never be read as a target. A projection is arithmetic on assumptions you supply. Real investments can fall as well as rise.
Worked example
A saver sets aside 8,000 now at 4.5% a year, compounded quarterly, for 25 years, and assumes 2% yearly inflation.
Inputs
| Amount today | 8000 |
|---|---|
| Annual interest rate | 4.5 % |
| Number of years | 25 |
| Interest compounded | Quarterly |
| Inflation (optional) | 2 % |
Result
8,000.00 invested for 25.00 years at 4.5% a year, compounded 4 time(s) a year.
| Growth earned | 16,487.44 |
|---|---|
| Growth multiple | 3.0609 times |
| Effective annual rate | 4.5765% |
| Value in today's purchasing power | 14,925.85 |
Growth by year
| Year | Growth so far | Value |
|---|---|---|
| Year 1 | 366.12 | 8,366.12 |
| Year 2 | 749.00 | 8,749.00 |
| Year 3 | 1,149.40 | 9,149.40 |
| Year 4 | 1,568.12 | 9,568.12 |
| Year 5 | 2,006.00 | 10,006.00 |
| Year 6 | 2,463.93 | 10,463.93 |
| Year 7 | 2,942.81 | 10,942.81 |
| Year 8 | 3,443.61 | 11,443.61 |
| Year 9 | 3,967.33 | 11,967.33 |
| Year 10 | 4,515.01 | 12,515.01 |
| Year 11 | 5,087.77 | 13,087.77 |
| Year 12 | 5,686.73 | 13,686.73 |
- Formula: FV = PV × (1 + rate ÷ n)^(n × years).
Financial disclaimer: Results are estimates for planning and education. They are not financial, tax or legal advice. Fees, taxes, rates and rules vary by lender, product and country, so confirm figures with your provider or a qualified adviser before making decisions.
Frequently asked questions
How do I calculate future value?
Multiply the present amount by one plus the periodic rate, raised to the total number of periods. At 5% yearly for 10 years the multiplier is 1.6289.
What is the difference between future value and present value?
Future value moves money forward in time using growth, while present value moves a future sum back to today using a discount rate. They are the same relationship seen from opposite ends.
What does continuous compounding mean?
It is the mathematical limit of compounding more and more often. The growth factor is e raised to rate times time, which is slightly above the daily compounding result.
Can future value be lower than the starting amount?
Yes, if the rate is negative. A negative rate models a loss or a charge that exceeds interest earned.
Should I include inflation?
If you care about what the money will buy, yes. Enter your inflation assumption to see the future value in today's purchasing power.
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References and sources
- Standard time-value-of-money texts: future value of a lump sum and continuous compounding.
- Investor.gov (U.S. SEC): background on compound interest. Link