Compound Interest Explained: The Formula, the Maths and 30 Years of It

Compound interest is interest paid on interest. You earn a return, the return is added to your balance, and next period's return is calculated on the bigger number. Do that for a few years and it barely registers. Do it for thirty and most of your money is money you never deposited.

That last sentence is the whole article, and it is arithmetic rather than magic. Here is the maths, properly shown.

The compound interest formula

A = P(1 + r/n)^(nt)

Read aloud: the final amount equals the starting amount, multiplied by (one plus the rate divided by the number of compounding periods), raised to the power of periods times years.

Substituting those in:

A = 10,000 × (1 + 0.05 ÷ 12) ^ (12 × 10) = 10,000 × 1.00416667^120 = 16,470.09

So 10,000 left alone for a decade at 5%, compounded monthly, becomes 16,470.09. You earned 6,470.09 without doing anything.

Simple interest — interest paid only on the original principal — would have paid 500 a year, so 5,000 over the decade, ending at 15,000. Compounding earned 6,470 instead of 5,000: 29% more interest.

Now run both out to 30 years on the same terms. Simple interest pays 15,000 and ends at 25,000. Compounding pays 34,677 and ends at 44,677. The advantage is no longer 29% — it is 131% more interest.

That widening gap is the only thing you actually need to understand. Every other section here is a consequence of it.

What 30 years of monthly saving actually does

Almost nobody has a lump sum sitting still. The realistic case is a regular monthly contribution, which uses a slightly different formula — the future value of an ordinary annuity:

A = PMT × [ ((1 + r/n)^(nt) − 1) ÷ (r/n) ]

Where PMT is the amount you pay in each period. With 300 a month, 6% a year compounded monthly, for 30 years:

A = 300 × [ (1.005^360 − 1) ÷ 0.005 ] = 300 × 1,004.515 = 301,354.51

You paid in 300 × 360 = 108,000. You finished with 301,354. Growth did 193,354 of the work — 64% of the final balance.

The maths is proportional, so the currency does not matter. $300, £300, €300, C$300 or A$300 a month at 6% for 30 years all produce the same multiple: 2.79 times what you paid in. Halve the contribution and you halve both numbers.

Whether that monthly figure is achievable is a separate question from the arithmetic. On the OECD's one comparable measure, households saved 5.7% of net disposable income in the US in 2024 and 4.7% in the UK — though a national saving rate is a whole-sector residual, not the share of anyone's payslip, so it sets the scale rather than the target.

Here is the shape of it, which is the part that argument alone never conveys.

Worked example

Contributions versus balance, 300 a month for 30 years

6% a year compounded monthly. Currency units — the ratios are identical in $, £, €, C$ or A$.

• Balance
• What you paid in

Show the data

Years of saving	Balance	What you paid in
0	0	0
5	20,931	18,000
10	49,164	36,000
15	87,246	54,000
20	138,612	72,000
25	207,898	90,000
30	301,355	108,000

Notice where the money comes from. In the first decade you contribute 36,000 and growth adds 13,164. In the third decade you contribute the same 36,000 and growth adds 126,743.

Worked example

Where the final 301,355 came from

300 a month at 6% a year, compounded monthly, over 30 years

108,000

Total paid in

+13,164

Growth, years 1-10

+53,448

Growth, years 11-20

+126,743

Growth, years 21-30

301,355

Balance at year 30

You can run your own numbers through the compound interest calculator, or work backwards from a target with the savings goal calculator.

Starting early beats contributing more

This is the claim every article on this topic makes and almost none of them shows. Two savers, same 300 a month, same 6%:

Worked example

Two savers, both retiring at 65

300 a month, 6% a year compounded monthly, no withdrawals

Starts at 25, stops at 35Pays in for 10 years, then never adds another penny

296,093balance at 65

• Total paid in36,000
• Years contributing10
• Years compounding after stopping30
• Growth260,093

Starts at 35, never stopsPays in every month for 30 straight years

301,355balance at 65

• Total paid in108,000
• Years contributing30
• Years compounding after stopping0
• Growth193,355

The early saver's 36,000 has thirty years of untouched compounding after the last deposit: 49,164 at age 35 grows by 1.005^360 to 296,093.

If you are in the ten-year window this chart is about, budgeting in your 20s and paying yourself first are the two habits that make the left-hand column possible. Neither requires large sums.

Compounding frequency: real, but smaller than the hype

This is the mechanical sub-question people actually search for, and the honest answer is that it matters less than the marketing implies. 10,000 at a 5% nominal rate for 10 years:

Worked example

Same principal, same rate, different compounding frequency

10,000 at a 5% nominal annual rate, held for 10 years

16,289

Annuallyn = 1

16,436

Quarterlyn = 4

16,470

Monthlyn = 12

16,487

Dailyn = 365

That is why the industry quotes an effective rate rather than the nominal one. A 5% nominal rate compounded monthly is an effective 5.12% a year; compounded daily it is 5.13%. In the UK that effective figure is the AER on savings and the APR on borrowing. In the US and Canada it is APY on deposits and APR on credit. Australia often shows a nominal rate plus the compounding frequency, so you have to do the conversion yourself.

Decision rule: compare AER against AER, or APY against APY. Comparing a nominal rate with an effective one always flatters the nominal one.

The rate does the heavy lifting

Frequency is worth a rounding error. The rate is worth a house deposit. Same 300 a month, same 30 years, same 108,000 paid in:

Four percentage points of rate more than doubles the outcome on identical contributions. That is the case for not leaving long-term money in a poorly-paying account — and, equally, the case for being sceptical of anyone promising the 7% row without explaining the risk attached to it.

The Rule of 72, and where it breaks

Divide 72 by the annual percentage rate to approximate the years to double. At 6%, 72 ÷ 6 = 12 years. It is an approximation, and it drifts:

It is most accurate around 8% and understates the doubling time badly at high rates — which matters mainly when you point it at credit card debt.

What rate can you actually get?

This is where the honest article separates from the optimistic one. The 5% and 6% figures above are illustrative. Real deposit rates as of mid-2026:

• In the US, the FDIC national average rate on savings accounts was 0.38% in July 2026, and 1.68% on a 12-month CD. At 0.38%, 10,000 becomes 10,191 after five years. Compounding cannot rescue a rate that low.
• In the UK, the Bank of England reports an effective rate of 4.30% on new fixed-term household deposits in June 2026, but just 1.65% across the existing stock of instant-access balances. Same country, same month, and the gap over five years on 10,000 is 12,343 versus 10,853.

Those two bullets contain the most useful action in this article: the money is usually in the wrong account, not earning the wrong kind of interest. Moving it is a fifteen-minute job. If the balance is an emergency fund rather than long-term savings, the emergency fund guide covers the access-versus-rate trade-off — you are deliberately giving up some rate for instant access, and that is the right call.

The rate compounding against you

Every projection above is in nominal terms. Prices compound too, and they compound against your balance.

Annual consumer price inflation, latest published

• USUnited States3.5%12 months to June 2026 (CPI-U)US Bureau of Labor Statistics
• UKUnited Kingdom2.6%12 months to June 2026 (CPI)Office for National Statistics
• CACanada2.8%12 months to June 2026Statistics Canada
• AUAustralia3.8%12 months to June 2026Australian Bureau of Statistics
• IEIreland3.4%June 2025 to June 2026Central Statistics Office Ireland

Work the arithmetic through. If prices rise 2.5% a year for 30 years — an assumption below every reading in the chart above, and closer to what most central banks target — that 301,355 balance buys what 143,669 buys today. The real return on a 6% nominal rate against 2.5% inflation is not 3.5% — it is (1.06 ÷ 1.025) − 1 = 3.41%. Run the same 300 a month for thirty years at that 3.41% real rate — which is the same as assuming you raise the contribution in line with prices each year — and you finish with 187,653 in today's money.

Still nearly twice what you paid in, in real terms. But it is 188,000, not 301,000, and any page showing you the larger number without this paragraph is selling something.

Compound interest in reverse

The same formula, pointed at you. Take the average US cardholder balance of $5,300 (CFPB, 2024) at the 22.15% average rate US commercial banks charged on accounts assessed interest in Q2 2026 (Federal Reserve G.19).

Month one interest: 5,300 × (0.2215 ÷ 12) = $97.83.

Those payoff figures are illustrative — minimum-payment formulas vary by issuer, and this one assumes 1% of the balance plus that month's interest with a $25 floor and no new spending. The direction of travel does not vary. Adding $50 a month to the payment cuts the interest by $1,317.

UK readers face the same mechanic. The Bank of England put the representative quoted rate on UK credit card lending at 24.71% in July 2026 — that is an advertised representative rate rather than an average of what borrowers actually pay, so it is not directly comparable with the US figure above, but it is plainly the same territory.

The practical consequence: none of the deposit rates in the section above comes close to what a card charges, so clearing high-rate debt returns more, and with far more certainty, than leaving the money on deposit. Debt snowball versus avalanche covers the ordering, and the credit card payoff calculator will do this arithmetic on your actual balance.

Where the model stops working

Four limitations worth naming, because pages that skip them are less trustworthy, not more.

"Compound interest" on investments is not interest. A savings account pays a contractual rate. A stock market return is compounding of reinvested dividends and price growth, and it is not guaranteed in any year. A 6% average over 30 years does not mean 6% in each of those 30 years — and sequence matters, because a bad decade early hurts more than a bad decade late.

Tax changes the effective rate. Which wrapper you hold money in usually matters more than a quarter-point of rate: an ISA in the UK, a 401(k), IRA or Roth in the US, a TFSA or RRSP in Canada, superannuation in Australia, a PRSA in Ireland. Rules and limits differ by country and change, so check the current position with your own tax authority rather than trusting any blog's figure.

Fees compound too. A 1% annual platform or fund charge is subtracted from the rate before compounding, and over 30 years it comes out of the growth column, not the contributions column.

Real life interrupts. Job loss, a house move and a new baby all interrupt monthly contributions, and every projection here assumes you never miss one. Making the budget stick is the unglamorous half of this that determines whether the chart above ever happens.

Frequently asked questions

Is compound interest better than simple interest?

For a saver, yes, and the advantage widens with time. On 10,000 at 5% compounded monthly, the compound balance beats the simple-interest balance by 1,470 after 10 years and by 19,677 after 30. For a borrower it is the reverse — compounding is what makes a revolving card balance so expensive.

How often should interest compound for it to be worth it?

Any frequency compounds. Going from annual to daily on 10,000 at 5% for 10 years adds about 198, or 1.2%. Prioritise the headline rate; treat frequency as a tie-breaker between two accounts paying the same AER or APY.

Does the Rule of 72 actually work?

It is accurate to within a few months for rates between roughly 4% and 10%, and it is most exact around 8%. Above 15% it understates the doubling time — at 20% it says 3.6 years when the answer is 3.8.

---

See the balance grow, not just the projection

iBudget tracks the money going in each month and what is left after the bills, so the contribution in the chart above is a number you actually hit rather than one you assumed.

Start budgeting free — free plan, no card required, no bank logins.