Compound interest — how it works and why time matters

Compound interest is a return earned not only on the money you put in, but also on the gains it has already made. PLN 10,000 at 7% a year is worth PLN 20,097 after 10 years, PLN 40,387 after 20 and PLN 81,165 after 30: the third decade adds more than the first two together. That's why time matters: PLN 500 a month from age 25 to 65 grows to PLN 1,312,407, but from age 35 only to PLN 609,986, although the difference in payments is just PLN 60,000 (amounts before tax and inflation).

How does compound interest work?

When interest is added to the capital — this is called capitalisation (kapitalizacja) — it earns together with the capital in the next period. So each new gain is calculated on a larger amount. At first the difference is small, but over time interest on interest becomes the main part of the result.

This is how PLN 10,000 paid in once grows at a 7% yearly return, before tax and inflation:

If the interest were paid out every year instead of being added to the capital (simple interest), the gain would be a flat PLN 700 a year: PLN 21,000 after 30 years. The rest of the gain — PLN 50,165, or 70% — is interest on interest.

That's why time is what matters most with compound interest. The rate of return decides how fast the amount grows, but it takes years for interest on interest to take over.

What is the compound interest formula?

Our compound interest calculator adds interest every month: the balance grows by a twelfth of the yearly return, and the interest joins the capital straight away. For a single payment this gives the formula:

FV = P × (1 + r/12)¹²ⁿ

FV is the final value, P the amount paid in, r the yearly return as a fraction (7% is 0.07) and n the number of years. For example, PLN 10,000 at 7% for 10 years: 10,000 × (1 + 0.07/12)¹²⁰ ≈ PLN 20,097.

Interest added every month starts earning sooner, so 7% a year works out at 7.23% a year in practice. Compounded once a year, PLN 10,000 would be worth PLN 76,123 after 30 years, not PLN 81,165.

With regular payments, the calculator adds each payment at the end of the month, after the interest. Payments of W a month are then worth this after n years:

FV = W × ((1 + r/12)¹²ⁿ − 1) ÷ (r/12)

At a zero return this formula doesn't work (division by zero), but then the result is simply the sum paid in. The calculator doesn't use ready-made formulas: it works month by month and rounds amounts to the grosz (0.01 zł), so its result can differ from the formula very slightly.

How do regular payments grow?

Compound interest works for regular saving too, except each payment works for a different length of time: the first month's for the whole period, the last month's not at all. Paying in PLN 500 a month for 30 years at 7% a year, you put in PLN 180,000 in total and end up with PLN 609,986. Of that, PLN 429,986, or 70%, is gain.

• Value before tax
• Total paid in

Chart data

Year	Total paid in	Value before tax	Gain
1	PLN 6,000	PLN 6,196	PLN 196
2	PLN 12,000	PLN 12,841	PLN 841
3	PLN 18,000	PLN 19,965	PLN 1,965
4	PLN 24,000	PLN 27,605	PLN 3,605
5	PLN 30,000	PLN 35,796	PLN 5,796
6	PLN 36,000	PLN 44,580	PLN 8,580
7	PLN 42,000	PLN 54,000	PLN 12,000
8	PLN 48,000	PLN 64,099	PLN 16,099
9	PLN 54,000	PLN 74,929	PLN 20,929
10	PLN 60,000	PLN 86,542	PLN 26,542
11	PLN 66,000	PLN 98,995	PLN 32,995
12	PLN 72,000	PLN 112,348	PLN 40,348
13	PLN 78,000	PLN 126,665	PLN 48,665
14	PLN 84,000	PLN 142,018	PLN 58,018
15	PLN 90,000	PLN 158,481	PLN 68,481
16	PLN 96,000	PLN 176,134	PLN 80,134
17	PLN 102,000	PLN 195,063	PLN 93,063
18	PLN 108,000	PLN 215,361	PLN 107,361
19	PLN 114,000	PLN 237,125	PLN 123,125
20	PLN 120,000	PLN 260,463	PLN 140,463
21	PLN 126,000	PLN 285,489	PLN 159,489
22	PLN 132,000	PLN 312,323	PLN 180,323
23	PLN 138,000	PLN 341,097	PLN 203,097
24	PLN 144,000	PLN 371,951	PLN 227,951
25	PLN 150,000	PLN 405,036	PLN 255,036
26	PLN 156,000	PLN 440,512	PLN 284,512
27	PLN 162,000	PLN 478,553	PLN 316,553
28	PLN 168,000	PLN 519,344	PLN 351,344
29	PLN 174,000	PLN 563,084	PLN 389,084
30	PLN 180,000	PLN 609,986	PLN 429,986

The total paid in grows in a straight line, the value faster and faster. In year 19 the gain first exceeds everything paid in so far. In year 30 the gain alone is PLN 40,902 — 6.8 times the PLN 6,000 you pay in that year.

What is starting earlier worth?

Take two people who each put away PLN 500 a month at a 7% yearly return until age 65. One starts at 25, the other 10 years later.

Starting 10 years earlier means PLN 60,000 more paid in, but PLN 702,421 more at the end. If the person who started at 25 stopped paying in at 35, their PLN 60,000 would be worth PLN 702,421 at 65 — more than the PLN 609,986 from 30 years of payments from age 35 (PLN 180,000). That is where the gap between the two plans comes from: the earliest payments work the longest.

To have as much at 65 as someone who started at 25, a person starting at 35 would need to pay in PLN 1,076 a month: 2.2 times as much.

If you're saving for retirement or financial independence, the FIRE calculator shows how much you need, and our guide to the 4% rule explains it.

The rule of 72: how long until your money doubles?

For a quick estimate of when your money doubles, divide 72 by the yearly return in percent. At 7% the rule of 72 gives 10.3 years (72 ÷ 7), and the exact result is 10.2 years with yearly compounding and 9.9 years with monthly compounding, as in the calculator. That is why the PLN 10,000 of the first example is worth a little over twice as much after 10 years: PLN 20,097.

The rule of 72 approximates yearly compounding: at 8% it hits the exact result, at 2, 4 and 6% it slightly overstates it, and at 10 and 12% it slightly understates it. With monthly compounding money doubles a little faster, because interest starts earning sooner.

The rule also works backwards: to double your money in 10 years you need about 7.2% a year (72 ÷ 10).

How much do fees and the Belka tax take?

Compounding works on costs too: money taken as a fee stops earning, and so does the interest it would have made. A fund's yearly fee lowers your return by roughly the size of the fee itself, so in this guide we simply count it as a lower return: a fund that earns 7% and charges 2% a year gives you about 5%. This is the plan of PLN 500 a month for 30 years at two levels of fees:

A 0.2% yearly fee cuts the result after 30 years by PLN 23,534, or 3.9%. A 2% fee takes PLN 193,856: 31.8% of the result and 45.1% of the gain.

The Belka tax is 19% of capital gains, but how much it really takes depends on when you pay it. The same plan, by how the tax is paid:

When you sell, for example fund units or accumulating ETFs, you pay 19% of the whole gain once, at the end: PLN 81,697. Until then the whole amount compounds, future tax included. When the tax is taken from interest as it is credited, as on a savings account, you pay less tax (PLN 68,422 instead of PLN 81,697), yet you keep less (PLN 471,695 instead of PLN 528,288). The bank withholds 19% of every interest payment, so only the rest keeps compounding — as if the return were 5.67% rather than 7% a year.

In an IKE (indywidualne konto emerytalne, an individual retirement account) there is no tax if you withdraw after age 60 (or after 55 with early-retirement rights), provided you paid in during at least 5 calendar years or over half of the payments were made at least 5 years before the withdrawal. Then you keep the whole PLN 609,986. IKE payments have a yearly limit. The IKE, IKZE or PPK calculator compares what you keep in each, and our guides to IKE or IKZE and the Belka tax go into more detail. The compound interest calculator opens this plan with tax on a sale.

What will it be worth after inflation?

We assume inflation of 3.5% a year, Poland's 2010–2025 average according to GUS, the national statistics office, rounded to one decimal place. The real value shows what the result would be worth in today's money: the calculator divides the amount by (1 + inflation)ⁿ, where n is the number of years.

With inflation at 3.5% a year, PLN 609,986 in 30 years will buy what PLN 217,325 buys today, or PLN 188,218 after tax on a sale. The real return, above inflation, is 3.60% a year: (1 + 7.23%) ÷ (1 + 3.5%) − 1. That is how fast your money really grows.

The rule of 72 works for prices too: with inflation at 3.5% they double roughly every 20.6 years (72 ÷ 3.5), exactly every 20.1 years. Money that earns no interest loses half its value in that time.

On the compound interest calculator page we note that over the long run shares have historically returned about 7–10% a year on average in nominal terms, but individual years vary a lot. A cautious assumption is 5–7% nominal, which — with monthly compounding, as in the calculator, and inflation at 3.5% — is about 1.6–3.6% a year in real terms. The 7% in this guide is the top of that cautious range.

The calculator assumes the same return every year. In reality returns change from year to year, so the result is an estimate, not a promise. Our guide to inflation and your savings covers how to protect savings from inflation.