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How to use this calculator#
- Enter what you already haveThe starting amount is the lump sum working from day one. Leave it at zero if you are beginning from nothing — the monthly contribution alone still compounds, it just has less time on the earliest deposits.
- Add the monthly contributionThis is the single most controllable input. Each contribution earns for the months remaining, not the whole term, which is why an extra $50 added today is worth far more than $50 added in year fifteen.
- Use a realistic rateSavings accounts and the headline return on an index fund are different animals. If you want the answer in today's spending power, enter the return minus inflation — 8% nominal becomes roughly 5% real.
- Set the compounding frequencyMonthly is the default and matches most savings accounts and funds. Switching from yearly to monthly on 8% raises the effective annual rate from 8% to 8.30% — real, but far smaller than one extra percentage point of return.
- Push the years out and watch the shapeCompounding is not a straight line. On $10,000 at 8% with no contributions, years 1–20 add $39,268 and years 21–40 add $193,466 — the second half of the timeline does five times the work of the first.
The formula#
Future value of a lump sum plus an ordinary annuity
FV = P(1 + r)ⁿ + PMT × [ (1 + r)ⁿ − 1 ] ÷ r
- FV
- Balance at the end of the term
- P
- Starting principal
- r
- Interest rate per compounding period: annual rate ÷ periods per year
- n
- Total number of compounding periods: years × periods per year
- PMT
- Contribution added at the end of each period
This is the ordinary-annuity form: each period earns interest first, then the contribution lands. Paying at the start of the period instead (an annuity due) multiplies the contribution part by a further (1 + r) and raises the answer by well under 1% at monthly rates. When r = 0 the second term is undefined — the total is simply P + PMT × n.
Why compound interest is so powerful#
Compound interest means you earn interest on your interest, not just your original deposit. Over long periods this creates exponential — not linear — growth.
The two biggest levers are time and rate: starting earlier and reinvesting returns matters more than almost anything else.
Worked examples#
$10,000 plus $200 a month at 8% for 20 years
A lump sum and a standing order, compounded monthly over two decades.
- Periodic rate r = 0.08 ÷ 12 = 0.00666667; periods n = 20 × 12 = 240
- (1 + r)ⁿ = 1.00666667²⁴⁰ = 4.926803
- Lump sum: 10,000 × 4.926803 = 49,268.03
- Annuity factor: (4.926803 − 1) ÷ 0.00666667 = 589.0204
- Contributions: 200 × 589.0204 = 117,804.08
- FV = 49,268.03 + 117,804.08 = 167,072.11
$167,072.11. Of that, $10,000 was the starting balance, $48,000 was contributed monthly, and $109,072.11 is growth.
The cost of starting ten years late
Two savers each put away $200 a month at 8% and stop at 65. One starts at 25, the other at 35.
- Starting at 25: n = 480 months, FV = 200 × [(1.00666667⁴⁸⁰ − 1) ÷ 0.00666667] = 698,201.57
- Starting at 35: n = 360 months, FV = 200 × [(1.00666667³⁶⁰ − 1) ÷ 0.00666667] = 298,071.89
- Extra contributed by starting early = 120 × 200 = 24,000
- Extra ending balance = 698,201.57 − 298,071.89 = 400,129.68
An extra $24,000 paid in produces an extra $400,130 at the end. The ten years you cannot buy back are worth about seventeen times the money they cost.
Reference tables#
| Years | 4% | 6% | 8% | 10% |
|---|---|---|---|---|
| 5 | $12,210 | $13,489 | $14,898 | $16,453 |
| 10 | $14,908 | $18,194 | $22,196 | $27,070 |
| 20 | $22,226 | $33,102 | $49,268 | $73,281 |
| 30 | $33,135 | $60,226 | $109,357 | $198,374 |
| 40 | $49,399 | $109,575 | $242,734 | $537,007 |
Every figure scales linearly: $50,000 at 8% for 30 years is 5 × $109,357 = $546,785.
| Years | 4% | 6% | 8% | 10% |
|---|---|---|---|---|
| 5 | $25,470 | $27,443 | $29,594 | $31,941 |
| 10 | $44,358 | $50,970 | $58,786 | $68,039 |
| 20 | $95,581 | $125,510 | $167,072 | $225,155 |
| 30 | $171,945 | $261,129 | $407,429 | $650,472 |
| 40 | $285,791 | $507,873 | $940,935 | $1,801,823 |
At 40 years you will have contributed $96,000 on top of the $10,000. Everything above $106,000 in each cell is compounding.
| Compounding | Effective annual rate | Balance after 20 years |
|---|---|---|
| Annually | 8.000% | $46,609.57 |
| Semi-annually | 8.160% | $48,010.21 |
| Quarterly | 8.243% | $48,754.39 |
| Monthly | 8.300% | $49,268.03 |
| Daily | 8.328% | $49,521.64 |
| Continuously | 8.329% | $49,530.32 |
The whole span from annual to continuous is worth $2,921 over 20 years. Moving the rate from 8% to 8.5% is worth more than every frequency upgrade combined.
| Annual return | Rule of 72 estimate | Exact years |
|---|---|---|
| 2% | 36.0 | 35.0 |
| 4% | 18.0 | 17.7 |
| 6% | 12.0 | 11.9 |
| 8% | 9.0 | 9.0 |
| 10% | 7.2 | 7.3 |
| 12% | 6.0 | 6.1 |
The shortcut is most accurate between 6% and 10% and drifts at the extremes. Exact years = ln(2) ÷ ln(1 + r).
Common mistakes#
- Entering a stock-market return for money you need soonAn 8% average is an average of violent years. Markets have fallen more than 30% inside twelve months more than once, so money needed within about five years belongs in cash or bonds where the projection is close to a promise rather than a hope.
- Reading a nominal projection as spending power$167,072 in 20 years buys roughly what $92,500 buys today at 3% inflation. Either enter a real return — nominal minus inflation — or mentally deflate the answer before deciding it funds anything.
- Forgetting tax and fees eat the rate, not the balanceA 0.9% platform-and-fund charge turns an 8% return into 7.1%. Over 30 years on $10,000 plus $200 a month, that drops the final balance from $407,429 to $332,486 — a $74,943 charge for nine tenths of a percent. The fee is a percentage of the pot, so it compounds against you exactly as returns compound for you.
- Assuming the growth curve is roughly straightPeople stop contributing in year eight because progress looks slow. On $10,000 at 8%, the first twenty years add $39,268 and the next twenty add $193,466. Quitting early forfeits the only part of the curve that was ever going to be dramatic.
Frequently asked questions#
What does compounding frequency mean?
It's how often earned interest is added to the balance. More frequent compounding (monthly vs annually) slightly increases the final amount.
Are contributions added before or after interest?
This calculator adds each contribution during the period and compounds the balance at the chosen frequency, a close model of most regular-savings plans.
Key terms#
- Compound interest
- Interest calculated on the principal plus all previously accumulated interest, so each period earns on a larger base than the last.
- Compounding period
- How often earned interest is added to the balance — daily, monthly, quarterly or annually. More frequent compounding raises the effective rate slightly.
- APY / effective annual rate
- The true yearly return once compounding is included. A nominal 8% compounded monthly is an APY of 8.30%. Compare accounts on APY, not the headline nominal rate.
- Ordinary annuity
- A stream of equal payments made at the end of each period. This calculator models contributions this way, which is how most standing orders and payroll deductions behave.
- Real return
- Nominal return minus inflation — what your money actually gains in purchasing power. A 6% return in a 4% inflation year is a 2% real return.
- Rule of 72
- Divide 72 by the annual return to estimate the years until money doubles. At 9% that is 8 years; the exact answer is 8.04.
Sources#
- Compound Interest Calculator and investor guidance — U.S. Securities and Exchange Commission (Investor.gov)
- How does compound interest work? — Consumer Financial Protection Bureau
- Truth in Savings (Regulation DD) — how APY is defined — Consumer Financial Protection Bureau
Figures last checked .
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