Compound Interest Calculator

What this calculator is, and when to reach for it

Compound interest is the only idea in personal finance that is genuinely difficult to feel. The arithmetic is simple — you earn a return, that return joins the balance, and next period you earn a return on the larger figure — but human intuition is stubbornly linear, and compound growth is not.

The consequence is that people consistently underestimate long-run outcomes and, more damagingly, underestimate what a few extra years at the start are worth. Money invested in your twenties does something that the same money invested in your forties cannot, and no amount of later diligence fully recovers it.

This calculator projects a starting amount, regular contributions, a rate you choose, and a length of time, and shows where the result comes from: how much you put in, and how much the growth added. That split is the whole point, because watching the second figure overtake the first is the clearest illustration of the idea.

Reach for it when you want to see what regular saving becomes, when comparing what an extra decade of time is worth against an extra amount each month, or simply to build an intuition for how the mechanism behaves.

The same mechanism, working against you

Everything on this page applies identically to debt, which is worth stating because it explains why card balances behave the way they do. Interest charged on interest is compound growth pointed in the other direction.

A borrower paying the minimum on a card is on the wrong side of exactly this curve: the balance generates interest, the interest joins the balance, and the effect accelerates. The same force that makes a modest monthly investment substantial over decades makes a modest debt intractable.

It is also why clearing high-rate debt reliably beats investing. Avoiding compound interest at twenty-something percent is mathematically identical to earning it, with none of the uncertainty.

Where to go next

For a projection framed around a portfolio rather than a savings balance, the investment return calculator covers the same mechanics with market assumptions in view. For a goal-based version, the retirement calculator compares a projection against a target and shows the gap.

To see the mechanism working against you, the minimum payment calculator shows what compounding does to a card balance, and the credit card payoff calculator shows what escaping it is worth.

On the borrowing side, the amortization calculator shows the same arithmetic applied to a loan, and the extra payment calculator shows why early overpayments are disproportionately effective — for exactly the reason early contributions are here.

How the projection is worked out

Two components, calculated separately and added: what the starting amount becomes, and what the stream of contributions becomes.

FV = PV(1 + r)ⁿ + PMT × [ ((1 + r)ⁿ − 1) ÷ r ]

PV

the amount you start with today

PMT

the amount added each period

r

the rate for one period, being the annual rate divided by periods per year

n

the total number of periods

Why the curve is not a line

In year one you earn a return on your contributions alone. In year twenty you earn a return on twenty years of contributions plus every return those contributions have already generated. The base grows, so the growth grows.

This is why projections look unremarkable early and startling late, and why people who stop at the five-year figure conclude the whole thing is overstated. The interesting part is structurally in the final third.

Time is the input that cannot be recovered

Rate and contribution are both things you can adjust. Time is not: a year that passes without contributions is a year of compounding permanently lost, and it is the year that would have had longest to work.

The practical consequence is unglamorous but real. Starting modestly and immediately reliably beats starting substantially and later, and the gap widens the longer the horizon.

Compounding frequency matters less than people expect

How often interest is credited — monthly, quarterly, annually — does affect the result, but the difference is modest compared with the rate, the contribution, and the time. Moving from annual to monthly compounding at a given rate produces a small improvement, not a transformation.

It is worth understanding because product marketing sometimes emphasises it, and because a quoted rate is not directly comparable across different compounding conventions. But it is a second-order input, not a lever worth optimising over.

What a steady rate assumption hides

The projection applies your chosen rate to every single period. Real returns do not behave that way, and for anything invested in markets the smooth curve is a simplification rather than a forecast.

It also excludes inflation, tax, and fees, all of which reduce what a projected figure is actually worth. A result stated in today’s money is worth considerably less in thirty years’ money, which is a distinction the retirement calculator handles explicitly.

What this page assumes

It grows your starting amount at the rate and compounding frequency you chose, then adds the growth on each recurring contribution from the end of the period in which it is paid in.

Contributions grow at the rate for one contribution period, converted from the compounding frequency you chose. Interest earned is the future value minus your starting amount and all of your contributions.

Worked examples, step by step

Take 10,000 to start, 500 added every month, a 7% annual rate compounding monthly, over twenty years.

Where the final figure comes from

The balance reaches 300,850.72, of which you contributed 130,000 and growth supplied 170,850.72. More than half the final figure was never deposited by you, which is the entire argument for starting.

Now look at the halfway point. After ten years the balance is 106,639.02, of which growth accounts for just 36,639.02 — barely a third. In the first decade you are doing most of the work; in the second, the balance is.

What the second decade actually does

Between year ten and year twenty the balance rises from 106,639.02 to 300,850.72, a gain of 194,211.70, while your contributions across that decade were only 60,000. The other 134,211 came from growth on money that was already there.

That asymmetry is the mechanism in a single comparison. Identical contributions, identical rate, and the later decade produced more than three times the growth of the earlier one — purely because it started from a larger base.

The cost of a ten-year delay

Someone who waits a decade and then contributes the same 500 a month for the remaining ten years finishes near 106,639 rather than 300,850. The delay costs almost 195,000, having saved 60,000 of contributions.

To catch up, the late starter would need to contribute roughly three times as much each month. That is the honest measure of what time is worth, and it is why the least useful advice is to wait until you can afford to save properly.

The vocabulary, on and around this page

Compound interest

Return earned on both the original amount and on returns already credited, so the base itself grows over time.

Simple interest

Return earned only on the original amount. The contrast that makes compounding’s effect visible over long periods.

Present value

The amount you start with today, before any contributions or growth are applied.

Future value

The projected balance at the end of the period, combining the grown starting amount and the grown contributions.

Periodic contribution

The amount added each period. Its earliest instalments contribute disproportionately because they compound longest.

Periodic rate

The annual rate divided by the number of compounding periods in a year, applied at each step.

Compounding frequency

How often returns are credited. It affects the outcome modestly compared with rate, contribution, and time.

Growth component

The portion of the final balance not contributed by you. Watching it overtake contributions is the clearest illustration of compounding.

Contribution total

Everything you deposited, including the starting amount. Comparing it against the final balance shows what compounding added.

Time horizon

The length of the projection, and the only input that cannot be increased retrospectively.

Rule of 72

A shortcut estimating doubling time by dividing 72 by the rate, useful for building intuition without a calculator.

Doubling time

How long a balance takes to double at a given rate. Each doubling adds more than all previous growth combined.

Real return

Growth after inflation. It is what determines purchasing power, and it is not modelled here.

Nominal return

Growth before inflation, which is what a quoted rate normally expresses and what this projection uses.

Opportunity cost of delay

What a postponed start costs. In the worked example, ten years of waiting cost almost 195,000.

Front-loaded contributions

Depositing more in the early years, which produces a materially larger outcome than the same total contributed later.

Negative compounding

The same mechanism applied to debt, where interest joins the balance and accelerates growth against you.

Fees drag

The compounding effect of charges, which reduces the growth component year after year. Not modelled here.

Volatility

Variation in actual returns around an average. A steady-rate projection smooths it away entirely.

Sequence of returns

The order in which gains and losses occur, which affects real outcomes but is invisible in a fixed-rate projection.

Common mistakes, and what this page will not do

• Judging the idea by the early years. After ten years growth supplied only a third of the example balance. After twenty it supplied more than half.
• Waiting until you can contribute a serious amount. A ten-year delay cost almost 195,000 in the example, having saved 60,000 of contributions. Time cannot be bought back later.
• Treating a steady rate as a forecast. The projection applies your rate to every period. Real market returns vary, and the smooth curve is a simplification.
• Reading the result in today’s money. Inflation is not modelled, so a figure decades out is worth substantially less than the same number today.
• Ignoring fees and tax. Both reduce the growth component and both compound. A projection gross of them overstates what you would actually hold.
• Optimising compounding frequency. Moving from annual to monthly crediting helps modestly. Rate, contribution, and time matter far more.
• Investing while carrying high-rate debt. Compounding runs against you on a card balance. Avoiding twenty-something percent reliably beats an uncertain market return.
• Assuming a higher rate compensates for a late start. It rarely does over realistic ranges, and chasing return to make up lost time usually means accepting risk that does not suit the goal.
• Stopping contributions when the balance looks large. The later decades produce the biggest gains precisely because the base is large. Interrupting them forfeits the most productive period.

What this calculator leaves out: This calculator applies one steady rate to every period and does not model inflation, tax, fees, market volatility, or the sequence in which returns occur. It projects a nominal figure from the starting amount, contribution, rate, and period you enter, and nothing shown is guaranteed.

Frequently asked questions