Compound Interest Calculator

How compound interest is calculated

Compound interest pays you interest on your interest. Each period, the balance earns a return, and that return is added back so the next period's interest is calculated on a larger amount. Over time this snowball effect makes the balance grow far faster than simple interest, which only ever pays on your original deposit. This calculator adds your monthly contribution to the balance as it goes, so contributions and compounding work together.

Formula

A = P(1 + r/m)^(m·t) + PMT × [((1 + i)ⁿ − 1) ÷ i]

where P is the starting amount, r the annual rate, m the number of compounding periods per year, t the number of years, PMT the recurring contribution, i the periodic rate, and n the number of contribution periods. The first term grows your initial deposit; the second grows the stream of contributions.

Worked example

$10,000 starting balance, $300 added monthly, 7% annual return, compounded monthly for 20 years:

• Total contributions: $10,000 + ($300 × 240) = $82,000
• Final balance: ≈ $196,000
• Interest earned: ≈ $114,000 — more than the money you put in.

The longer the money stays invested, the larger the interest slice becomes. Starting five years earlier often beats contributing more later, because those early deposits have the most time to compound.

How far simple and compound interest drift apart

Simple interest is charged only on the original amount; compound interest is charged on the original amount plus whatever interest has already accrued. The structural difference sits in the exponent — simple interest multiplies by time, compound interest raises to the power of time. Over a year that is worth nothing. Over a decade it decides the outcome.

$10,000 at 6%:

At one year the two are identical — compounding has had nothing to compound yet. By 30 years compound interest has produced $29,435 more on the same deposit, and the interest earned is 164% larger. The divergence is slow at the start, which is exactly why it is easy to dismiss.

Which kind applies to your product

That last row is the one to watch. A flat-rate loan charges interest on the original amount even as you repay it, so the effective rate is close to double the quoted one — a "10% flat" loan over a year works out near 18–19% APR, because on average you only had half the money for half the time.

APR and APY: the same rate, described differently

The convention is not accidental: loans are advertised with the smaller-looking number and savings with the larger one. To compare two products honestly, put both on the same basis first:

APY = (1 + APR ÷ n)ⁿ − 1

Time beats rate, and it is not close

Because time sits in the exponent and rate does not, an extra decade usually outperforms an extra percentage point. $10,000 invested once:

Put the other way: at 7%, someone who invests $200 a month from 25 to 35 and then stops entirely ends up with about $281,000 at 65. Someone who starts at 35 and keeps going for thirty years ends up with about $244,000. The first put in $24,000; the second put in $72,000. Ten years of head start beat three times the money.

How accurate the rule of 72 is

years to double ≈ 72 ÷ interest rate as a percentage

It is accurate to within a few months between about 4% and 12%, which covers most real decisions. It works in reverse too: at 3% inflation, prices double in 24 years, which is why a pension projected in today's money needs adjusting.

Where the projection stops being reliable

• Inflation. A 7% return with 3% inflation is a real return of about 3.9%. $76,123 in thirty years buys roughly what $31,000 buys today.
• Fees compound too. A 1% annual fee on a 7% return does not cost you 1%; over 30 years it removes roughly a quarter of the final balance, because the fee is charged on the compounding balance every year.
• Tax. Interest taxed every year cannot fully compound. The same rate inside a tax-sheltered account substantially outperforms the same rate outside one.
• Returns are not a fixed rate. Markets deliver an average, not an annuity. A bad decade at the start of retirement withdrawals does far more damage than the same decade at the end.

Every compound interest formula in one place

P is the starting amount, r the annual rate as a decimal, n the compounding periods per year, t the years, and in the contributions formula i is the rate per period and N the total number of periods. Depreciation is the same equation with the sign flipped — a car losing 15% a year is compound interest running backwards.

Compounding frequency: monthly, half-yearly, daily

The stated rate is annual; n decides how often it is applied. More frequent compounding pays slightly more, with diminishing returns that stop mattering quickly.

The whole gap from annual to daily is $312 over a decade — about 1.7%. Frequency is worth understanding and rarely worth choosing a product over; the rate and the contributions dominate everything.

Worked examples over 2 and 3 years

Take $5,000 at 8% compounded annually:

Simple interest would have paid $400 every year, for $6,200. The $98.56 difference after three years is the whole idea — and it is why the curve on the chart bends upward rather than running straight.

Compound interest in Excel and Google Sheets

FV is the built-in future value function and it expects payments as negative numbers, because money leaving your pocket is a negative cash flow. Omitting the minus signs returns a negative balance.

The same maths on debt

Compounding is direction-neutral. On a credit card at 22% APR compounded daily, an untouched $3,000 balance grows to about $3,738 in a year — the same equation that builds savings, working against you. This is why paying down high-interest debt usually beats investing the same money: the guaranteed 22% you stop paying is larger than the return you would expect to earn.

Dividend reinvestment behaves the same way in reverse: reinvested payouts buy more shares, which pay more dividends. That is compounding even though nobody calls it interest.

Paying off debt instead? The loan payment calculator applies the same compounding math in reverse to show what borrowing costs you.