Future value formula
The future value of a single sum is FV = PV × (1 + i)N, where i is the rate per period and N the number of periods.[1] $5,000 at 6% for 10 years: 5,000 × 1.0610 = 5,000 × 1.790848 = $8,954.24.
The factor (1 + i)N is the future value factor. A few of them:
| Rate | 5 years | 10 years | 20 years | 30 years |
|---|---|---|---|---|
| 3% | 1.1593 | 1.3439 | 1.8061 | 2.4273 |
| 5% | 1.2763 | 1.6289 | 2.6533 | 4.3219 |
| 7% | 1.4026 | 1.9672 | 3.8697 | 7.6123 |
| 10% | 1.6105 | 2.5937 | 6.7275 | 17.4494 |
Future value of an annuity
The future value of an annuity, a series of equal payments, is PMT × [((1 + i)N − 1) ÷ i] when each payment comes at the end of a period (an ordinary annuity). If payments come at the start (an annuity due), each one earns one more period of interest, so multiply by (1 + i).[2]
| $1,000 a year at 6% for 10 years | Future value |
|---|---|
| Ordinary annuity (end of year) | $13,180.79 |
| Annuity due (start of year) | $13,971.64 |
| Paid in | $10,000 |
Paying at the start of each year adds $790.85 here: exactly 6% of the ordinary result.
Lump sum and payments together
When you have both, add the two future values. $5,000 now plus $100 a month at 6% compounded monthly for 10 years is $9,096.98 from the lump sum and $16,387.93 from the payments: $25,484.92 in total. This calculator assumes payments and compounding share one schedule; when they differ (monthly deposits, daily compounding), the compound interest calculator converts the rate for you and adds a chart.
Future value in a spreadsheet
Excel and Google Sheets use the same formula: =FV(rate, nper, pmt, pv, type), with rate per period, a negative sign on money you pay in, and type 1 for payments at the start. The last example is =FV(6%/12, 120, -100, -5000, 0) = $25,484.92.
Common mistakesUsing the annual rate with monthly periods (divide it by 12), mixing up ordinary and due annuities, and treating an assumed rate of return as a guarantee: investment returns vary from year to year.
To go the other way and find what a future sum is worth today, use the present value calculator. For a quick doubling estimate, the rule of 72; for income from stocks with reinvested dividends, the dividend calculator; investor.gov's compound interest calculator uses the same math.[3]
Related calculators
- Present value calculatorWhat a future sum or payment stream is worth today
- Compound interest calculatorDeposits, any compounding, inflation, goal seek, chart and CSV
- Rule of 72 calculatorDoubling time, and how far off the shortcut is
- Savings goal calculatorMonthly deposit needed for a target, or time to reach it
Frequently asked questions
What is the future value formula?
FV = PV(1 + i)N for a single sum. For regular payments add PMT × [((1 + i)N − 1) ÷ i], times (1 + i) if payments are at the start of each period.
What is the future value of $10,000 in 10 years?
It depends on the rate: at 5% compounded yearly it is $16,288.95; at 7% it is $19,671.51.
What is the difference between an ordinary annuity and an annuity due?
Payments in an ordinary annuity are made at the end of each period; in an annuity due, at the start. An annuity due is worth (1 + i) times as much.
How do I calculate future value in Excel?
Use =FV(rate, nper, pmt, pv, type), entering money you invest as negative numbers and the rate per period.