Money
Compound Interest Calculator
Enter a starting amount, a rate and a term. What compounding adds is shown as its own figure.
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)
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?
- Whichever question you are asking, but do not mix them. Enter the nominal rate and the answer is in future dollars; subtract inflation first and the answer is in today’s purchasing power, which is usually the more honest number for a twenty-year projection. This page does not model inflation, tax or fees, all three of which reduce the result.