Future Value Calculator
What a lump sum, regular deposits, or both together grow to at a given rate.
Last updated
Your details
Deposited at the end of each period.
Result
- Future value
- $21,589.25
- Total put in
- $10,000.00
- Growth earned
- $11,589.25
- Growth factor
- 2.1589×
After 10 periods at 8.00%
115.89% on what you put in
Applies to the opening amount
$10,000.00 growing at 8.00%…
FV = PV × (1 + r)ⁿ
r = 8.00% = 0.0800, n = 10
(1 + 0.0800)^10 = 2.158925
$10,000.00 × 2.158925
FV = $21,589.25
Formula — written step by step
10,000 growing at 8% for 10 years…
FV = PV(1+r)ⁿ + PMT × ((1+r)ⁿ − 1) ÷ r
r = 8% = 0.08, n = 10
(1.08)¹⁰ = 2.158925
10,000 × 2.158925 = 21,589.25
No regular deposits, so the annuity term is zero
FV = 21,589.25
PV is what you start with, PMT what you add each period, r the rate per period and n the number of periods. The first term grows the opening sum; the second grows the stream of deposits.
A worked example
Saving 500 a month for twenty years
- Starting amount
- 0
- Monthly deposit
- 500
- Return
- 7% a year, or 0.5833% a month
- Periods
- 240 months
- r = 0.07 ÷ 12 = 0.00583333
- (1.00583333)²⁴⁰ = 4.038739
- Annuity term = (4.038739 − 1) ÷ 0.00583333 = 520.9267
- FV = 500 × 520.9267
FV = 260,463.33
You deposited 120,000 over those twenty years; the other 140,463 is growth. The crossover — where accumulated growth first exceeds total deposits — happens around year fourteen, which is why stopping early costs so much more than the deposits you skip.
How to use this calculator
- Enter what you have today. Leave it at zero if you are starting from nothing and only making regular deposits.
- Enter what you add each period, if anything. Deposits are treated as arriving at the end of each period.
- Make the rate and the number of periods match: an annual rate with years, or a monthly rate with months. Mixing them is the most common mistake here.
- Compare the future value against the total you put in — the gap between them is what the growth actually contributed.
The two halves of the formula
Future value has two independent parts. The first grows a lump sum you already hold: multiply it by one plus the rate, raised to the number of periods. The second grows a stream of equal deposits, and is the part people find less intuitive, because each deposit compounds for a different length of time.
The annuity term handles that automatically. The first deposit of a twenty-year plan compounds for almost twenty years; the last compounds for none at all. Summing that series gives ((1+r)ⁿ − 1) ÷ r, which is what the formula multiplies the deposit by.
Why the rate matters more than the amount
Growth is exponential in the rate and only linear in the starting sum. Doubling what you begin with doubles the result; adding three percentage points to a forty-year return can triple it. This is the single most useful thing the formula teaches.
It also explains why fees are so damaging over long horizons. A one percent annual charge does not cost one percent of your final balance — over forty years at a 7% gross return it removes roughly a quarter of it, because the charge compounds against you every year exactly as the growth compounds for you.
What a constant rate hides
The formula assumes the same return every period. Real markets do not behave that way, and the order in which returns arrive matters whenever money is being added or withdrawn. Two sequences with an identical average can produce noticeably different balances.
Treat the result as a projection under stated assumptions rather than a forecast. It is most useful for comparing scenarios — this deposit against that one, this term against a longer one — where the assumption applies equally to both sides and largely cancels out.
Formula & methodology
What this calculator assumes
- Deposits are made at the end of each period (an ordinary annuity). Depositing at the start instead multiplies the annuity term by (1 + r) and produces a larger result.
- Assumes a constant rate every period. Real returns vary, and a sequence averaging the same rate can end at a very different figure.
- Excludes tax on the growth and any charges deducted by the provider.
Sources
- Brealey, Myers & Allen, Principles of Corporate Finance, 13th edition, McGraw-Hill, 2019 — compounding and annuities.
What 10,000 grows to
| Years | At 4% | At 7% | At 10% |
|---|---|---|---|
| 5 | 12,167 | 14,026 | 16,105 |
| 10 | 14,802 | 19,672 | 25,937 |
| 20 | 21,911 | 38,697 | 67,275 |
| 30 | 32,434 | 76,123 | 174,494 |
| 40 | 48,010 | 149,745 | 452,593 |
Over forty years, three percentage points of extra return turns 48,010 into 149,745 — and six points turns it into nearly half a million. Compounding rewards the rate far more than it rewards the starting sum.
Frequently asked questions
Should the rate be annual or monthly?
Whichever matches your periods. For monthly deposits, divide the annual rate by twelve and count months. Entering an annual rate against a monthly count is the most common error and overstates the result enormously.
Are deposits made at the start or end of the period?
At the end, which is the ordinary annuity convention. Depositing at the start of each period instead gives every deposit one extra period of growth, raising the result by a factor of (1 + r).
Does this account for inflation?
No. The figure is in nominal money. To see it in today’s purchasing power, use a real rate — roughly your expected return minus expected inflation — instead of the nominal one.
What if the rate is zero?
The formula still works: with no growth, the future value is simply the opening amount plus every deposit. The calculator handles this case rather than dividing by zero.