Future Value Calculator
- Updated
- Formula shown
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Results
$10,000.00 today plus $500.00 a month at 6% compounded monthly is worth $264,122.49 in 20 years
- Amount today
- $10,000.00
- Payments
- $120,000.00
- Interest or growth
- $134,122.49
| Year | Paid in | Interest | Value |
|---|---|---|---|
| 1 | $16,000.00 | $784.56 | $16,784.56 |
| 2 | $6,000.00 | $1,203.02 | $23,987.58 |
| 3 | $6,000.00 | $1,647.28 | $31,634.86 |
| 4 | $6,000.00 | $2,118.95 | $39,753.81 |
| 5 | $6,000.00 | $2,619.71 | $48,373.52 |
| 6 | $6,000.00 | $3,151.35 | $57,524.87 |
| 7 | $6,000.00 | $3,715.79 | $67,240.66 |
| 8 | $6,000.00 | $4,315.04 | $77,555.70 |
| 9 | $6,000.00 | $4,951.25 | $88,506.94 |
| 10 | $6,000.00 | $5,626.70 | $100,133.64 |
The rate is held constant. Savings rates change and investment returns vary from year to year, so treat the result as a projection, not a promise.
How to use the future value calculator
- Choose a lump sum on its own, or a lump sum plus regular payments.
- Enter the amount you have today. For payments, add the amount, how often you pay and whether each payment is at the start or the end of its period.
- Enter the annual interest rate or expected return, how often it compounds, and the number of years.
- Read the future value, how much of it comes from the starting amount and from the payments, and the yearly table.
Future value formulas
Payments at the end (ordinary annuity): FV = PMT × [(1 + i)n − 1] ÷ i
Payments at the start (annuity due): FV = PMT × [(1 + i)n − 1] ÷ i × (1 + i)
PV is the amount today, PMT the regular payment, i the rate per payment period and n the number of payments. With monthly payments and monthly compounding, i is the annual rate ÷ 12 and n is years × 12. When the compounding and payment schedules differ, i is converted so the effective annual rate stays the same.
With both a lump sum and payments, the future value is simply the two results added together. The annuity formula is the sum of a geometric series: the first payment grows for n − 1 periods, the next for n − 2 and so on, with the last payment earning nothing. Moving every payment to the start of its period gives each one an extra period of growth, which is the (1 + i) factor.
Worked examples
- Lump sum: $10,000 at 6% compounded monthly for 20 years grows to $10,000 × 1.005240 = $33,102.04.
- Adding payments: $500 at the end of each month for the same 20 years grows to $231,020.45. Together with the $10,000, the future value is $264,122.49, of which $130,000 is money paid in.
- Timing: $1,000 a year for 10 years at 5% grows to $12,577.89 with payments at the end of each year, or $13,206.79 with payments at the start.
Future value of monthly payments at 5%
Payments at the end of each month, 5% compounded monthly, no starting balance. The rate is an example, not a forecast.
| Monthly payment | After 10 years | After 20 years | After 30 years |
|---|---|---|---|
| $100 | $15,528 | $41,103 | $83,226 |
| $250 | $38,821 | $102,758 | $208,065 |
| $500 | $77,641 | $205,517 | $416,129 |
| $1,000 | $155,282 | $411,034 | $832,259 |
Each row is a straight multiple of the first, because the formula is proportional to the payment: double the payment, double the future value. Time works differently. Going from 20 to 30 years adds more than the first 10 years did, because growth builds on growth.
Using future value well
- Rates on investments are assumptions. A savings account rate is known today but can change; stock and fund returns vary a lot from year to year. Try a cautious rate as well as a hopeful one.
- Think in today's money. A future balance buys less if prices rise. The interest calculator shows an inflation-adjusted value.
- Work backwards when you have a target. The savings calculator finds the monthly amount a goal needs, and the present value calculator finds what a future sum is worth now.
Frequently asked questions
How do you calculate future value?
For a lump sum, FV = PV × (1 + i)^n, where i is the rate per period and n the number of periods. $10,000 at 6% compounded monthly for 20 years grows to $10,000 × 1.005^240 = $33,102.04.
How do you calculate the future value of regular payments?
Use FV = PMT × [(1 + i)^n − 1] ÷ i for payments at the end of each period. $500 a month at 6% compounded monthly for 20 years grows to $231,020.45, from $120,000 of payments.
What is the difference between an ordinary annuity and an annuity due?
In an ordinary annuity each payment is made at the end of the period; in an annuity due it is made at the start, so every payment grows for one extra period. $1,000 a year for 10 years at 5% grows to $12,577.89 as an ordinary annuity and $13,206.79 as an annuity due.
What rate should I use for an investment?
Any rate for an investment is an assumption, because returns are not guaranteed and vary from year to year. Try a range, such as a cautious and an optimistic rate, and treat the results as scenarios rather than predictions.
Does compounding frequency change the future value?
Yes, more frequent compounding gives a slightly higher result for the same nominal rate. 6% compounded monthly is an effective 6.17% a year. If you know the effective annual return, choose annual compounding and enter that rate.