What is compound interest?

Interest paid on interest already earned. Simple interest on $10,000 at 6% pays $600 every year for ever; compound interest pays $600 in the first year and 6% of $10,600 in the second. Over twenty years the gap on that sum alone is around $11,100 — which this page prints as its own figure.

Does it matter when I make the monthly contribution?

A little. This page assumes it lands at the end of each period, which is the conservative assumption and what most savings plans do. Paying at the start of each period earns one extra period of interest on every payment — worth roughly the rate divided by the number of periods, so under half a percent at monthly compounding.

Should I use the nominal rate or the real one?

Enter the nominal rate — the one your account quotes — and read both answers side by side. The balance is in future dollars; the figure beside it converts that balance into today’s purchasing power at the inflation rate you set, which is usually the more honest number for a twenty-year projection. Tax and fees are still not modelled, and both reduce the result.

Money

Compound Interest Calculator

Enter a starting amount, a rate and a term. What compounding adds is shown as its own figure.

The link carries your figures, so it reopens on exactly these numbers.

When your money starts doing the work

In year 18, the interest you have earned overtakes everything you have paid in. From then on the account grows more from its own returns than from your contributions.

It takes that long because interest compounds on a balance that starts small. Nothing about the first years suggests the last ones.

If the return is not the one you entered

Nobody knows a twenty-year return in advance. One point either way, on the same contributions, changes the ending by this much.

If returns are lower
$109,333.14
at 5% · $51,333 interest
At the return you entered
$125,510.22
at 6% · $67,510 interest
If returns are higher
$144,572.72
at 7% · $86,573 interest

The large figure is the final balance; the smaller one is the interest inside it.

Where the balance comes from

Scale tops out at $125,510

Year 1Year 20

Interest earnedWhat you paid inInterest overtakes contributions, year 18

Year by year

Each year: what you have paid in, the interest earned, the balance, and what it is worth in today’s money
Year	Paid in	Interest	Balance	In today’s money
1	$12,400	$684	$13,084	$12,827
2	$14,800	$1,558	$16,358	$15,723
3	$17,200	$2,634	$19,834	$18,690
4	$19,600	$3,924	$23,524	$21,733
5	$22,000	$5,443	$27,443	$24,856
6	$24,400	$7,202	$31,602	$28,062
7	$26,800	$9,218	$36,018	$31,356
8	$29,200	$11,507	$40,707	$34,743
9	$31,600	$14,085	$45,685	$38,227
10	$34,000	$16,970	$50,970	$41,813
11	$36,400	$20,181	$56,581	$45,506
12	$38,800	$23,738	$62,538	$49,310
13	$41,200	$27,662	$68,862	$53,232
14	$43,600	$31,976	$75,576	$57,277
15	$46,000	$36,705	$82,705	$61,451
16	$48,400	$41,873	$90,273	$65,759
17	$50,800	$47,508	$98,308	$70,208
18Interest passes contributions here.	$53,200	$53,638	$106,838	$74,804
19	$55,600	$60,295	$115,895	$79,554
20	$58,000	$67,510	$125,510	$84,465

The formula

r = annual rate ÷ 100 ÷ compounds per year

n = years × compounds per year

lump sum: balance = principal × (1 + r)^n

contributions: + monthly × ((1 + r)^n − 1) ÷ r (when they match the compounding period)

The page steps the account forward period by period rather than applying the closed form, because a schedule and a chart need every intermediate year. A test checks the two agree.

Worked example

$10,000 plus $200 a month, 6% a year compounded monthly, for 20 years

r = 0.06 ÷ 12 = 0.005 per month, n = 240
The $10,000 alone becomes $33,102
The $200 a month becomes $92,408
Total $125,510, of which $58,000 was paid in

Where this goes wrong

Believing the frequency of compounding matters much

It barely does, and the belief distracts from what does. $10,000 at 6% for 20 years is $32,071 compounded annually, $33,102 monthly and $33,201 daily — a 3.5% spread between the extremes. The rate and the number of years are worth vastly more: one extra percentage point on the same 20 years adds about $6,700, and five extra years adds about $11,600. Choose on the rate and the term, not on the compounding schedule.

Questions

What is compound interest?: Interest paid on interest already earned. Simple interest on $10,000 at 6% pays $600 every year for ever; compound interest pays $600 in the first year and 6% of $10,600 in the second. Over twenty years the gap on that sum alone is around $11,100 — which this page prints as its own figure.
Does it matter when I make the monthly contribution?: A little. This page assumes it lands at the end of each period, which is the conservative assumption and what most savings plans do. Paying at the start of each period earns one extra period of interest on every payment — worth roughly the rate divided by the number of periods, so under half a percent at monthly compounding.
Should I use the nominal rate or the real one?: Enter the nominal rate — the one your account quotes — and read both answers side by side. The balance is in future dollars; the figure beside it converts that balance into today’s purchasing power at the inflation rate you set, which is usually the more honest number for a twenty-year projection. Tax and fees are still not modelled, and both reduce the result.