How future value works
Future value answers one question: if money grows at a steady rate and you keep adding to it, how much is there at the end? The formula has two parts. The starting amount grows by compound interest: FV = PV × (1 + r)^n, where r is the rate per period and n is the number of periods. The monthly contributions grow as an annuity: each $200 earns interest from the month it is paid, so the contributions together are worth PMT × (((1 + r)^n − 1) / r). Add the two parts and you have the future value. At the defaults the rate per month is 7% divided by 12, which is 0.5833%, and the number of months is 20 times 12, which is 240. The starting amount grows by a factor of 4.038739, and the contributions grow by an annuity factor of 520.926660 — each $1 a month becomes $520.93. The interest is the future value minus everything you put in: $144,572.72 minus $58,000 is $86,572.72. Notice where the interest comes from: the starting amount earns $30,387.39 of it, and the monthly contributions earn $56,185.33 of it — the contributions earn more interest than the lump sum, because there are 240 of them and the early ones have 20 years to grow.
The worked example, line by line
Setup: starting amount $10,000, monthly contribution $200, annual rate 7%, 20 years, compounded monthly.
Line 1 — monthly rate. 7% / 12 = 0.5833% a month (0.0058333).
Line 2 — periods. 20 years × 12 = 240 months.
Line 3 — growth factor. (1 + 0.0058333)^240 = 4.038739.
Line 4 — starting amount grows to. $10,000 × 4.038739 = $40,387.39.
Line 5 — annuity factor. (4.038739 − 1) / 0.0058333 = 520.926660.
Line 6 — contributions grow to. $200 × 520.926660 = $104,185.33.
Line 7 — future value. $40,387.39 + $104,185.33 = $144,572.72.
Line 8 — what you put in. $10,000 + ($200 × 240) = $58,000.
Line 9 — interest earned. $144,572.72 − $58,000 = $86,572.72.
Every branch, checked
10 years: half the time, far less than half the money — $54,713.58, with $34,000 contributed and $20,713.58 of it interest. The second 10 years adds $89,859.14, because compounding accelerates: the balance is bigger, so the same 7% is worth more each year.
No monthly contribution: the $10,000 alone grows to $40,387.39 — $30,387.39 of it interest. The monthly $200 is worth $104,185.33 of the total, which is almost three quarters of the final balance. A lump sum alone grows steadily; regular contributions are what make the total large.
At 5%: the total falls to $109,333.14 — $35,239.58 less than at 7% — with $51,333.14 of it interest. Two percentage points cost more than a third of the interest, because the rate compounds 240 times: a small change in the rate, repeated 240 times, is a large change in the outcome.
Annual compounding: the same inputs with interest added once a year — contributions grouped as $2,400.00 at each year-end — give $137,086.03, which is $7,486.69 less than monthly compounding. Monthly compounding wins because each contribution starts earning interest sooner, and interest is added 12 times a year instead of once.
30 years: $325,159.17, with $82,000 contributed and $243,159.17 of it interest. Ten more years nearly triples the interest, from $86,572.72 to $243,159.17 — the last decade does more work than the first two combined, because the balance is so much larger by then.
The reverse question: what do I need to save?
The calculator also answers the question backwards: how much a month do you need to reach a target? With $10,000 starting, 7% a year compounded monthly, and 20 years, reaching $100,000 takes $114.44 a month. The working is the same formula solved for the monthly contribution: the target minus what the starting amount grows to, divided by the annuity factor. The starting amount grows to $40,387.39, so the contributions must supply the other $59,612.61, and $59,612.61 divided by the annuity factor of 520.926660 is $114.44 a month. At exactly $114.44 the balance lands at $100,002.24 — $2.24 past the target, because the contribution is rounded to cents. Put in $114.44 a month and you contribute $37,465.60 over 20 years, on top of the $10,000 start, and interest earns the remaining $62,536.64. The reverse question is the useful one for planning: pick the target first, then read off the monthly habit it takes.
Monthly vs annual compounding
Compounding frequency is worth $7,486.69 at the defaults — $144,572.72 monthly against $137,086.03 annually — but the reason is smaller than it looks. Monthly compounding adds interest 12 times a year, so each month’s contribution starts earning sooner, and the interest itself starts earning interest a month earlier. Annual compounding waits until the year-end to add anything, so the money sits idle for up to 11 months. The gap grows with the rate and the time: at 3% over 20 years it would be far smaller, and at 7% over 30 years it would be far larger. In practice, most savings accounts and funds compound monthly or daily, so the monthly figure is the realistic one — the annual figure is here so you can see what the frequency is worth, not because your bank uses it. What matters far more than the frequency is the rate and the years: 2 percentage points of rate cost $35,239.58, and 10 extra years add $180,586.45.
Rounding convention, stated plainly: the future value is computed from the unrounded monthly rate (7% divided by 12) and the unrounded growth and annuity factors, then rounded to cents — so $10,000 times 4.038739 is $40,387.39 and $200 times 520.926660 is $104,185.33, and the two add to $144,572.72. The interest is the rounded future value minus the rounded total contributed. Monthly contributions are treated as paid at the end of each month; annual compounding groups them as $2,400.00 at each year-end.
Output · formula · meaning
| Output | Formula | What it means |
|---|
| Future value | PV(1+r)^n + PMT × (((1+r)^n − 1)/r) | $144,572.72 in 20 years. |
| You contribute | $10,000 + $200 × 240 | $58,000.00 put in by you. |
| Interest earned | $144,572.72 − $58,000 | $86,572.72 earned by interest. |
| Starting amount alone | $10,000 × 4.038739 | $40,387.39 — the lump sum on its own. |
| Contributions alone | $200 × 520.926660 | $104,185.33 — the monthly $200 grown. |
| 10 years | same inputs, n = 10 | $54,713.58 — $34,000 contributed, $20,713.58 interest. |
| No monthly contribution | PMT = 0 | $40,387.39 — $30,387.39 of it interest. |
| At 5% | same inputs, r = 5% | $109,333.14 — $35,239.58 less than at 7%. |
| Annual compounding | $2,400 at each year-end | $137,086.03 — $7,486.69 less than monthly. |
| To reach $100,000 | solve for PMT | $114.44 a month — lands at $100,002.24. |
| 30 years | same inputs, n = 30 | $325,159.17 — $82,000 contributed, $243,159.17 interest. |
Who uses this
- The 20-year saver: starts with $10,000 and adds $200 a month, and learns the balance becomes $144,572.72 — with interest earning $86,572.72, more than the $58,000 put in.
- The 10-year planner: has a 10-year horizon and learns the same habit reaches only $54,713.58 — less than half the 20-year total, because compounding needs time to accelerate.
- The lump-sum checker: wonders what the $10,000 does alone and learns it becomes $40,387.39 — the monthly $200 is worth $104,185.33 of the total, nearly three quarters of the final balance.
- The target-setter: wants $100,000 in 20 years and learns the monthly habit is $114.44 — $37,465.60 contributed over 20 years, with interest earning the remaining $62,536.64.
Accuracy & limitations
The math is exact for the numbers you enter: the future value is the starting amount times the growth factor plus the monthly contribution times the annuity factor, with the monthly rate as the annual rate divided by 12 and the number of periods as the years times 12; the interest is the future value minus everything contributed. But the inputs carry the assumptions, and they are strong ones. The rate is constant — real investments do not return 7% every year, and a bad decade early on changes the outcome far more than a bad decade late. Contributions are paid at the end of each month and never change — no raises, no skipped months, no withdrawals. Taxes, fees, and inflation are not counted: $144,572.72 in 20 years buys less than $144,572.72 today, and a real account pays tax on the gains and fees to the fund. Annual compounding groups the monthly contributions as $2,400.00 at each year-end, which is an approximation of a once-a-year schedule, not a different product. This page is a planning calculator, not investment advice — it shows what a steady rate and a steady habit would do, not what any real investment will do. For the printed reference tables, see the future value tables and the future value factor table.
Cite this calculatorBright Side Kit. “Future Value Calculator: See What Your Money Grows To.”
brightoolbox.com, 2026. Method: FV = PV(1+r)^n + PMT × (((1+r)^n − 1)/r), monthly compounding, r = annual rate / 12, n = years × 12, contributions at month-end. Defaults: PV $10,000, PMT $200/month, 7%, 20 years → FV $144,572.72, contributed $58,000, interest $86,572.72. Branches: 10 years $54,713.58; no contribution $40,387.39; 5% $109,333.14; annual compounding $137,086.03; $100,000 target takes $114.44/month. Related tables:
future value tables,
future value factor table.
Bright Side Kit. "Future Value Calculator: See What Your Money Grows To" https://brightoolbox.com/future-value-calculator/ Accessed October 24, 2026. Embed this calculatorPaste this into any web page to embed the live calculator. The “Powered by Bright Side Kit” link below it must stay intact.