Compound interest calculator

What this works out

Compound interest is interest earned on interest already earned. Over a few years the effect is modest. Over a few decades it is most of the outcome, and the point at which it overtakes your own contributions is later than nearly everyone guesses.

This calculator answers two questions at once: what the balance becomes, and how much of it you put there yourself. The second number is the one that usually surprises people.

The method

The annual return is divided by the number of compounding periods in a year to give a periodic rate, then converted into an equivalent monthly growth factor. That conversion is what lets contributions arrive monthly while interest is credited annually, quarterly, monthly or daily, without needing four separate calculations.

Each month the balance is multiplied by that factor and then the contribution is added. Adding afterwards means a payment does not earn interest during the month it arrives, which is the standard treatment for an ordinary annuity and errs slightly on the cautious side.

If an inflation rate is given, the final balance is divided by compounded inflation over the same period. That converts a future amount into today’s money, which is a different question from reducing the rate of return, and the one people usually mean.

Before you read on

Start with 10,000, add 250 a month, leave it 20 years at 5% compounded monthly. You will have paid in 70,000. What is the balance?

• AAbout 85,000 — twenty years is not that long.

  That is roughly what a simple-interest account would do. Compounding is the difference.

• BAbout 130,000 — a little under half of it is growth.

  Yes: 129,884.82, of which 59,884.82 was never paid in.

• CAbout 250,000 — the balance more than trebles.

  That needs either a higher rate or a longer run. At 5% over 20 years the money does not quite double against what went in.

129,884.82, of which 70,000 is money you paid in and 59,884.82 is growth — 46% of the final balance. The reason it is not more is that most of the contributions have not been invested for very long: the 250 paid in the last month earns nothing at all, and everything contributed in the second decade has had barely half the run to compound over.

• What you paid in70,00053.9%
• Growth59,884.8246.1%

A worked example

The figures below carry no currency symbol on purpose: the arithmetic is the same in pounds, euros or dollars, and the tool follows whichever currency your locale uses.

Start with 10,000, add 250 a month, assume 5% a year compounded monthly, and leave it for 20 years.

Balance after 20 years	129,884.82
Total you paid in	70,000.00
Interest earned	59,884.82

So a little under half the final balance is growth. Check it against the closed form for an ordinary annuity:

FV = P(1+i)^n + PMT x ((1+i)^n - 1) / i

i = 0.05/12,  n = 240,  (1+i)^n = 2.712640

  10,000 x 2.712640              =  27,126.40
  250 x (1.712640 / 0.0041667)   = 102,758.42
                                   -----------
                                    129,884.82

These are the same numbers asserted in this tool’s test file, so if the formula ever changes without this page changing with it, the build fails.

What it does not do

It assumes a steady return, level contributions, and no tax or fees. Every one of those makes the real figure lower than the one shown, so treat the result as an upper bound on a smooth path rather than a forecast. The assumptions are listed in full below.

The same formula run against money you owe rather than money you hold is a loan. For a balance that is being paid down instead of built up, mortgage repayment amortises it on the identical arithmetic.

monthlyFactor = (1 + r/n) ^ (n/12)

For each of the 12 x years months:
  balance = balance x monthlyFactor + contribution

where
  r  = annual return, as a decimal
  n  = compounding periods per year (1, 4, 12 or 365)

Present value, when an inflation rate is given:
  real = balance / (1 + i) ^ years