Future Value Calculator
Future value projects what an amount today becomes later. It is the mirror of present value and the more intuitive of the two, which is exactly why its assumptions get less scrutiny.
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FV = PV × (1 + r)^n (a single amount)
FV = PMT × [((1 + r)^n − 1) ÷ r] (a stream of contributions)
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The Two Cases Behave Differently
A lump sum grows exponentially and its result is dominated by time. A contribution stream
grows closer to linearly at first and only bends late, because the early contributions are
the only ones that have had time to compound.
| $10,000 today at 7% | $200/month at 7% |
|---|---|
| 10 yr: $19,672 | 10 yr: $34,617 |
| 20 yr: $38,697 | 20 yr: $104,185 |
| 30 yr: $76,123 | 30 yr: $243,994 |
| 40 yr: $149,745 | 40 yr: $525,704 |
Regular contributions overtake a modest lump sum quickly. This is the argument against
waiting until you have "enough to start".Ordinary Annuity or Annuity Due
Contributions at the *end* of each period (ordinary annuity) are the default. Contributions
at the *start* (annuity due) get one extra period of growth each, worth roughly one
additional period's return over the whole projection — a few percent, and easy to get wrong
in a spreadsheet.
Every Projection Is a Set of Assumptions
The output looks precise and is not. Three things move it:
The rate. 6% versus 8% over 30 years is a 70% difference in the result.- Sequence. The formula assumes a constant return; real markets deliver a sequence, and
for a contribution stream the order matters.
- Inflation. A nominal projection overstates purchasing power. Subtract inflation from
the rate to get an answer in today's money.Run the projection at a pessimistic rate as well as an expected one. A plan that only works
at 10% is not a plan.
The Projection Behind This Page
Starting from $10,000, adding $200 a month at 7%:
Year Deposited Balance Growth Growth on deposits 1 $12,400 $13,201 $801 6% 5 $22,000 $28,495 $6,495 30% 10 $34,000 $54,714 $20,714 61% 20 $58,000 $144,573 $86,573 149%
After 20 years, 60% of the balance is growth rather than money you
put in. That crossover — the point where returns exceed contributions — is the whole reason
compounding is worth waiting for, and it arrives later than most people expect.The Formula
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A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) ÷ (r/n)]
└── initial principal ──┘ └────── regular contributions ──────┘
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The second term usually dominates. On these numbers the $200 monthly contribution
accounts for the larger share of the final balance, which is the practical lesson: how much
you add matters more than the rate, right up until the balance gets large.
How Long Until It Doubles
The Rule of 72 divides 72 by the rate to estimate doubling time. At 7%:
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72 ÷ 7 = 10.3 years
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The exact answer is 10.2 years — the rule is accurate to within a few months
for rates between 6% and 10%, and drifts at the extremes. It works because ln(2) ≈ 0.693 and
72 has convenient divisors.
| Rate | Rule of 72 | Exact |
|---|---|---|
| 2% | 36.0 yr | 35.0 yr |
| 5% | 14.4 yr | 14.2 yr |
| 7% | 10.3 yr | 10.2 yr |
| 10% | 7.2 yr | 7.3 yr |
| 15% | 4.8 yr | 5.0 yr |
Compounding Frequency at This Rate
A nominal 7% turns into a different effective yield depending on how often it
compounds — this page uses annually:
| Compounded | Effective annual yield |
|---|---|
| Annually | 7.000% |
| Quarterly | 7.186% |
| Monthly | 7.229% |
| Daily | 7.250% |
| Continuously | 7.251% |
The gap between annual and monthly is worth having. The gap between monthly and daily is
0.021 percentage points — rounding. Compare accounts on
APY, which already folds the frequency in, rather than on the nominal rate.Inflation Is the Number That Matters
A 7% nominal return against 3% inflation is a 4.0% real return.
Real return is what buys anything:
`
real ≈ nominal − inflation
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Over 10 years, 3% inflation cuts purchasing power by about 26%. A projection quoted in nominal dollars therefore overstates what the money will actually be worth, which is why retirement targets are usually stated in today's dollars.