📈 Compound Interest Calculator
A compound interest calculator with contributions on their own schedule, the effective annual rate, a today's-money figure and exact doubling time.
- You put in
- $58,000.00
- Interest earned
- $86,572.72
- Interest as a share of the total
- 59.9%
- Effective annual rate (APY)
- 7.229%
- Principal doubles in
- 9.93 years
- Rule of 72 estimate
- 10.29 years
| Year | Start | Added | Interest | End |
|---|---|---|---|---|
| 2 | $10,000 | $4,800 | $1,834 | $16,634 |
| 4 | $16,634 | $4,800 | $2,828 | $24,262 |
| 6 | $24,262 | $4,800 | $3,971 | $33,033 |
| 8 | $33,033 | $4,800 | $5,285 | $43,118 |
| 10 | $43,118 | $4,800 | $6,796 | $54,714 |
| 12 | $54,714 | $4,800 | $8,533 | $68,046 |
| 14 | $68,046 | $4,800 | $10,530 | $83,376 |
| 16 | $83,376 | $4,800 | $12,826 | $101,003 |
| 18 | $101,003 | $4,800 | $15,467 | $121,270 |
| 20 | $121,270 | $4,800 | $18,503 | $144,573 |
What Compound Interest Calculator Does
Compound interest is interest that earns interest. The distinction sounds small and is not: $10,000 at 7% earns $700 in the first year under either scheme, but under compounding the second year earns 7% of $10,700, and forty years later the same deposit is worth $163,114 rather than the $38,000 simple interest would give.
What people usually want to know is what regular saving adds, and that is where most calculators — including the one this page replaced — get the arithmetic wrong. A monthly deposit and a daily compounding schedule are two different clocks, and treating them as one produces answers that are wrong by an order of magnitude. Contributions here run on their own frequency, converted through the effective annual rate so the two schedules stay consistent.
The other thing worth knowing before you tune anything is which inputs actually matter. Compounding frequency, which calculators make a prominent dropdown, is almost irrelevant: at 6% nominal, monthly compounding yields 6.1678% and daily 6.1831%, a difference of about fifteen dollars a year on a hundred thousand. Time and the rate itself are where the money is.
And a projection in nominal dollars flatters itself. A million dollars in thirty years buys roughly what $476,700 buys today at 2.5% inflation. That figure is shown alongside the headline so the number you plan around is one you can actually spend.
How to Use Compound Interest Calculator
- Enter the starting amount, annual rate and number of years
- Set the compounding frequency, from annual through to continuous
- Add a regular contribution and choose its own frequency — it does not have to match the compounding
- Read the future value, the effective annual rate, the inflation-adjusted figure and the year-by-year table
Formula Used by Compound Interest Calculator
The compound interest formula
A = P(1 + r/n)^(nt)
- P
- Principal — the starting amount
- r
- Nominal annual rate as a decimal, so 7% is 0.07
- n
- Compounding periods per year
- t
- Years
Worked example
$1,000 at 6% for 2 years, compounded annually then daily
- Annually: 1000 × 1.06² = 1,123.60
- Daily: 1000 × (1 + 0.06/365)^730 = 1,127.49
Result: $3.89 apart over two years — the compounding dropdown matters far less than it looks
Continuous compounding — the ceiling
A = Pe^(rt)
- e
- Euler’s number, about 2.71828
- Why it is a ceiling
- (1 + r/n)^n converges to e^r as n grows without bound
Worked example
The same $1,000 at 6% for 2 years
- 1000 × e^(0.06 × 2)
- e^0.12 = 1.127497
Result: $1,127.50 — one cent more than daily compounding, and no frequency can ever beat it
Adding regular contributions
A = P(1+E)^t + PMT × [((1+i)^(kt) − 1) ÷ i]
- E
- Effective annual rate, (1 + r/n)^n − 1
- k
- Contributions per year — independent of the compounding frequency
- i
- Rate per contribution period, (1+E)^(1/k) − 1
- Start of period
- Multiply the annuity term by (1+i) for deposits made at the start
Worked example
$10,000 at 5% compounded annually, plus $100 a month for 20 years
- Lump sum: 10,000 × 1.05²⁰ = 26,532.98
- Effective monthly rate: 1.05^(1/12) − 1 = 0.004074
- Annuity on 240 payments: 40,580
Result: About $67,113 — of which $34,000 is money you put in
Effective annual rate, and doubling time
APY = (1 + r/n)^n − 1 · doubling = ln(2) ÷ ln(1 + APY)
- APY
- What you actually earn in a year — the only number that compares accounts fairly
- Rule of 72
- The mental shortcut: 72 ÷ rate, closest to correct near 8%
Worked example
8% compounded annually
- ln(2) ÷ ln(1.08) = 9.0065 years
- 72 ÷ 8 = 9 years
Result: The shortcut is off by about two and a half days at 8%, and gets worse in both directions from there
Compounding frequency barely matters
A 6% nominal rate under every compounding schedule. The whole range from annual to continuous is 18 basis points — less than the gap between two competing savings accounts.
| Compounded | Periods per year | Effective annual rate | On $100,000 |
|---|---|---|---|
| Annually | 1 | 6.0000% | $6,000.00 |
| Semiannually | 2 | 6.0900% | $6,090.00 |
| Quarterly | 4 | 6.1364% | $6,136.36 |
| Monthly | 12 | 6.1678% | $6,167.78 |
| Biweekly | 26 | 6.1763% | $6,176.32 |
| Weekly | 52 | 6.1800% | $6,180.00 |
| Daily | 365 | 6.1831% | $6,183.13 |
| Continuously | ∞ | 6.1837% | $6,183.65 |
Where the Rule of 72 works and where it fails
Years to double at each annual rate, compounded annually. The shortcut is calibrated for the middle of this range and drifts at both ends.
| Rate | Exact years | Rule of 72 | Error |
|---|---|---|---|
| 1% | 69.66 | 72.00 | +2.34 years |
| 2% | 35.00 | 36.00 | +1.00 |
| 4% | 17.67 | 18.00 | +0.33 |
| 6% | 11.90 | 12.00 | +0.10 |
| 8% | 9.01 | 9.00 | −0.01 |
| 10% | 7.27 | 7.20 | −0.07 |
| 15% | 4.96 | 4.80 | −0.16 |
| 20% | 3.80 | 3.60 | −0.20 |
Why time beats everything else
$10,000 at 7% compounded monthly, with and without $200 a month. Note the last column: interest overtakes contributions somewhere in the second decade and never looks back.
| Years | Lump sum alone | With $200/month | You contributed | Interest share |
|---|---|---|---|---|
| 10 | $20,097 | $54,714 | $34,000 | 37.9% |
| 20 | $40,387 | $144,573 | $58,000 | 59.9% |
| 30 | $81,165 | $325,159 | $82,000 | 74.8% |
| 40 | $163,114 | $688,077 | $106,000 | 84.6% |
Simple against compound on the same deposit
$10,000 at 7%. Simple interest is a straight line; compound interest is an exponential, and the gap is the entire argument for starting early.
| Years | Simple interest | Compounded annually | Difference |
|---|---|---|---|
| 5 | $13,500 | $14,026 | $526 |
| 10 | $17,000 | $19,672 | $2,672 |
| 20 | $24,000 | $38,697 | $14,697 |
| 30 | $31,000 | $76,123 | $45,123 |
| 40 | $38,000 | $149,745 | $111,745 |
How to Read Your Result
The compounding dropdown is the least important input
Calculators put compounding frequency front and center, which gives the impression it is a lever worth pulling. It is not. Every schedule from annual to continuous fits inside 18 basis points at a 6% nominal rate — about fifteen dollars a year on a hundred thousand. The rate matters enormously, the time horizon matters more, and the amount you keep adding matters most of all. If you are choosing between two accounts, compare their APY and ignore how they got there.
APY exists so you cannot be misled by the frequency
A nominal rate is incomplete without knowing how often it compounds, which is precisely why US institutions must quote APY on deposit accounts. A 6% rate compounded monthly is a 6.17% annual return, and the same 6.17% compounded once a year is identical in every respect that matters. Once both accounts are expressed as APY, the comparison is honest and the compounding schedule becomes an implementation detail.
Interest overtakes your contributions, eventually
The crossover is the thing worth planning around. Saving $200 a month on top of $10,000 at 7%, interest accounts for 38% of the balance after a decade, 60% after two and 85% after four. The first decade feels like nothing is happening because it mostly is not — you are building the base the compounding will later act on. Stopping at year ten because the returns look unimpressive forfeits the part where the growth actually arrives.
Start of period against end of period
A deposit made at the start of each period earns one extra period of interest before the next one arrives, and those extra periods compound. On $10,000 at 5% with $100 a month over twenty years the gap is around $170 — small, but free. Payroll deductions typically settle at the end of a period; a standing transfer on the first of the month is a start-of-period deposit. Setting the option to match reality is worth doing if you are comparing scenarios closely.
Nominal projections quietly overstate the result
A balance of one million dollars in thirty years is not a million dollars of buying power. At 2.5% inflation it is worth about $476,700 in today's terms — less than half. The rate that matters for planning is the real rate, roughly the nominal return minus inflation, and over a working lifetime that distinction is the difference between a plan that works and one that only looks like it does. Every projection here shows both figures for that reason.
What the model deliberately leaves out
A constant rate is a modeling convenience, not a description of markets. Real returns arrive in an uneven sequence, and the order matters: a bad decade at the start of drawdown does far more damage than the same decade earlier, which averages cannot capture. Taxes on interest, account fees, and the practical difficulty of never touching the balance all reduce the outcome further. Treat the number as an upper bound under stated assumptions rather than a forecast.
Limitations & Accuracy Notes
- The rate is assumed constant for the whole term. Real investment returns vary year to year, and the sequence in which they arrive changes the outcome even when the average is identical.
- Taxes and fees are not modeled. Interest in a taxable account is generally taxable in the year earned, and an annual fee of even half a percent compounds against you over decades.
- Contributions are assumed to continue unchanged for the full term. There is no escalation for pay rises, and no allowance for missed months.
- The inflation adjustment applies one constant rate to the final balance. It converts the future figure to today's buying power; it does not inflate your contributions along the way.
- Results are a mathematical projection under the assumptions you enter, not a forecast and not financial advice. Deposit accounts have insured limits and investments can lose value.
- Continuous compounding is included because it is the limit of the formula and appears in finance coursework. Almost no retail product actually uses it.
Frequently Asked Questions
What is the compound interest formula?
Does daily compounding beat monthly by much?
What is APY and why does it differ from the stated rate?
How accurate is the Rule of 72?
Should contributions be at the start or end of the period?
Why show an inflation-adjusted figure?
References & Further Reading
- US Securities and Exchange Commission — Compound Interest Calculator (Investor.gov) — The SEC's own investor-education calculator, and the highest-authority tool ranking for this term
- Consumer Financial Protection Bureau — Regulation DD, Truth in Savings (12 CFR 1030) — The US rule requiring deposit institutions to disclose annual percentage yield, which is why APY rather than the nominal rate is the comparable figure
- Calculator.net — Compound Interest Calculator — Source of the formula treatment and the worked examples reproduced exactly here: $1,000 at 6% for two years giving $1,123.60 annually, $1,127.49 daily and $1,127.50 continuously
- Federal Reserve — Selected Interest Rates (H.15) — The Federal Reserve’s weekly release of US benchmark rates, for grounding the rate assumption in something current rather than a guess
- TheCalculatorSite — Compound Interest Calculator — The most feature-complete competing tool; its published $26,532.98 and $1,628.89 figures were used to verify the corrected contribution arithmetic