Compound Interest Calculator
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$10,000
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About the Compound Interest Calculator
Compound interest is what happens when returns are earned on returns. Simple interest pays a fixed amount on the original principal forever; compound interest folds each period's gain back into the balance so the next period earns on a larger base. Over a year or two the difference is trivial. Over thirty years it is the entire story.
The gap is easy to underestimate because the growth curve is exponential and human intuition is linear. $10,000 at 7% simple interest for 30 years reaches $31,000. The same $10,000 compounded annually at 7% reaches $81,165 — two and a half times as much, from the identical rate and the identical starting sum. Nothing was contributed; the difference is entirely interest earning interest.
Most real situations also involve regular contributions, and that changes which lever matters. When you are adding money every month, the balance is driven by contributions early on and by compounding later. The crossover — the point where cumulative growth exceeds cumulative deposits — typically arrives somewhere between years 12 and 18 at ordinary market returns. Quitting before that point means you paid the cost of saving without collecting the benefit.
Formula
A = P(1 + r/n)^(nt) + PMT × [ ((1 + r/n)^(nt) − 1) / (r/n) ]
- A
- Final balance
- P
- Starting principal
- PMT
- Contribution added each compounding period
- r
- Annual interest rate as a decimal — 7% is 0.07
- n
- Compounding periods per year (12 for monthly, 1 for annual)
- t
- Number of years
The expression has two independent halves. The first term, P(1 + r/n)^(nt), grows the money you started with. The second term is the future value of an annuity: it grows each contribution for however long that particular contribution has been invested, then sums them.
The second half is where the counterintuitive behaviour lives. A deposit made in year one is multiplied by the full growth factor; a deposit made in the final year is multiplied by almost nothing. Two people who contribute the same total amount can end up with wildly different balances purely from ordering.
This form assumes contributions arrive at the end of each period (an ordinary annuity). Contributions made at the start of each period earn one extra period of growth, which multiplies the annuity term by (1 + r/n) — worth about 0.6% more at 7% monthly. Small, but it is the reason payroll deductions early in the month beat late ones.
Worked Examples
$10,000 left alone for 30 years at 7%
No contributions. Just a lump sum in a broad index fund at a 7% annual return, compounded annually.
Result: $81,164.97
The money multiplied 8.1× without a single additional deposit. Simple interest at the same rate would have produced $31,000 — the extra $50,165 is purely interest compounding on interest.
$10,000 plus $500 a month for 30 years
The same starting balance, but now with a $500 monthly contribution and monthly compounding at 7%.
Result: $691,150.47
You deposited $190,000 and finished with $691,150. Investment growth of $501,150 accounts for 73% of the final balance — but only because it had three decades to accumulate.
The cost of starting ten years late
Identical $500 a month at 7%, but begun in year 11 instead of year 1 — a 20-year run rather than 30.
Result: Ten years of delay costs $390,300 for $60,000 of skipped contributions
The final decade generated $6.50 of balance for every $1 deposited during it, because it was compounding on top of everything that came before. Time in the market is doing more work than the contribution rate.
How to Use the Result
Compounding frequency matters far less than people assume
Marketing copy makes much of daily compounding. The actual effect is small and rapidly hits a ceiling. Take $10,000 at 7% for 10 years:
- —Compounded annually: $19,671.51
- —Compounded monthly: $20,096.61 — an extra $425
- —Compounded daily: $20,136.18 — an extra $40 on top of monthly
- —Compounded continuously: $20,137.53 — the mathematical limit, $1.35 above daily
Why the frequency ceiling exists
As n grows, (1 + r/n)^n converges to e^r. That limit is reached quickly: monthly compounding already captures about 91% of the total available gain over annual, and daily captures 99.7%. Choosing a bank for daily rather than monthly compounding is worth roughly 0.02 percentage points of effective yield.
The number that actually settles the comparison is APY (annual percentage yield), which folds compounding frequency into a single figure. Compare APY to APY and frequency stops mattering. Comparing a quoted nominal rate at one bank against an APY at another is where people get misled.
Nominal returns versus what you keep
A 7% projection is a nominal, pre-tax, pre-fee number. Three deductions apply before it becomes spendable:
- —Inflation — at 3% average inflation, 7% nominal is about 3.9% real. The $691,150 above has roughly $285,000 of today's purchasing power in 30 years.
- —Fees — a 1% expense ratio does not cost 1%, it compounds against you. On the 30-year example it removes about $120,000, because you lose the growth on every dollar of fee as well.
- —Tax — in a taxable account, dividends and realized gains are taxed annually, which interrupts compounding. Tax-advantaged accounts (401(k), IRA, ISA) preserve the full curve, which is most of their value.
The Rule of 72 as a sanity check
Dividing 72 by the annual rate approximates the doubling time in years. At 7%, 72 / 7 ≈ 10.3 years per doubling. Over 30 years that is roughly three doublings, so $10,000 should land near $80,000 — which matches the exact answer of $81,165 closely enough to catch an order-of-magnitude input error immediately.
The approximation is accurate between about 4% and 12%. Outside that band it drifts; at 2% the true doubling time is 35 years rather than the 36 the rule predicts, and at 25% it is 3.1 years rather than 2.9.
Edge Cases and Common Mistakes
A 0% rate makes the annuity term undefined
The contribution formula divides by r/n, so a zero rate produces a division by zero. The correct answer is trivially P + (PMT × n × t) — you get back exactly what you put in. Any calculator that returns an error or infinity at 0% is failing this case rather than telling you something meaningful.
Average return is not the same as actual return
This formula applies a constant rate. Real markets do not deliver one. A portfolio that gains 50% then loses 50% has an arithmetic average return of 0% but has actually lost 25% of its value. Sequence matters, and it matters most when you are withdrawing rather than contributing.
For long accumulation periods with steady contributions, the constant-rate projection is a reasonable central estimate. For retirement withdrawal planning it is actively misleading, and you want a sequence-of-returns or Monte Carlo model instead.
Contribution timing shifts the result by about half a percent
Contributing at the beginning of each period rather than the end adds one extra compounding period to every deposit. On the 30-year monthly example that is roughly $4,000 — small in relative terms but free, which is why front-loading an annual IRA contribution in January beats spreading it across the year.
Frequently Asked Questions
What return rate should I actually use?
For broad equity index funds over long horizons, 7% nominal (about 10% historical minus 3% inflation, or 10% nominal if you prefer to handle inflation separately) is the conventional planning figure. For bonds, 3% to 5%. For a savings account, use the quoted APY. Running your projection at your assumed rate minus 2% is a cheap way to see how fragile the plan is.
What is the difference between APR and APY?
APR is the nominal annual rate before compounding is applied. APY is the effective rate after compounding. A 6% APR compounded monthly is a 6.17% APY. Lenders quote APR because it looks lower; savings accounts quote APY because it looks higher. For comparing savings products, APY is the only number that is directly comparable.
Should I invest a lump sum or spread it out?
Mathematically, lump sum wins about two-thirds of the time, because markets rise more often than they fall and money invested earlier compounds longer. Dollar-cost averaging reduces the regret if you happen to buy at a peak. The formula above assumes whatever schedule you enter; it does not have a view on which is wiser.
How do taxes change these numbers?
In a tax-deferred account, nothing — you get the full curve and pay income tax on withdrawal. In a Roth or ISA, nothing, and withdrawals are untaxed. In a taxable account, annual tax on dividends and realized gains creates a drag of roughly 0.5% to 1.5% per year depending on turnover, which over 30 years can consume 15% to 30% of the final balance.
Why does my bank statement not match this projection?
Usually one of three things: the bank compounds daily but credits monthly, the advertised rate is promotional and has reverted, or the balance dipped below a tier threshold. Check the effective APY on the statement against the rate you entered — they are frequently different.
Does this work for debt as well as savings?
Yes, and it is worth doing. Credit card interest compounds in exactly the same way, typically daily at 20% to 30% APR. A $5,000 balance at 24% left untouched for three years grows past $10,000. The same mathematics that builds wealth slowly on the way up destroys it quickly on the way down, because the rate is three times higher.