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Compound interest calculator

Project a starting balance and any regular contributions forward at a rate you set, with the compounding frequency of your choice and a year-by-year table of the growth.

What you are starting with

Leave blank if you are starting from nothing

A year, as quoted

How often interest is paid into the balance

Regular contributions

Optional. Leave blank for none.

Contributions are added at the end of each period, after that period’s interest.

Projected balance

—

Enter a rate, a term and either a starting balance or a regular amount.

Why the last years are the big ones

Compound interest pays interest on interest. In the first year of a 6% account, 10,000 earns about 600. In the twentieth year the same account earns about 1,800, not because the rate changed, but because the balance earning it is three times larger. The year-by-year table above makes this visible: the interest column rises every year without anything extra being paid in.

That is also why time matters more than the amount. Ten years of contributions left to grow for twenty more will usually beat twenty years of the same contributions started ten years later, even though the second person paid in twice as much.

Nominal rates and effective rates

A rate quoted as 12% compounded monthly does not earn 12% over the year. It earns 1% a month, and each month’s interest starts earning too, which comes to 12.68% by the end. That figure is the effective annual rate, and it is shown in the results because it is the only honest way to compare two accounts that compound differently.

Compounding frequency matters far less than people assume. Moving from yearly to monthly compounding at 6% adds about 1.6% to a ten-year balance. Moving from monthly to daily adds about another tenth of a percent. An extra half a percent on the rate beats any change of frequency.

What this projection leaves out

  • Tax. Interest is taxable in most places, sometimes at source. Nothing is deducted here.
  • Fees. Platform and fund charges come straight out of the return. One percent a year against a six percent return removes about a fifth of the growth over a decade, and nearer a third over thirty years.
  • Inflation. Every figure is at face value. A balance that has doubled over twenty years at 3% inflation buys around 11% more, not 100% more.
  • Variation. The rate is applied unchanged for the whole term. Savings rates move, and investment returns vary enormously year to year.

Reading it honestly

This is arithmetic on an assumption, which makes it good for comparing plans against each other, this contribution against that one, this term against a longer one, and poor as a prediction of any single outcome. If the projection is for an investment rather than a deposit account, run it again at a rate two or three points lower and treat the gap between the two as the honest range.

Questions

What is compound interest?
Interest paid on your interest as well as on your original balance. Simple interest on 1,000 at 5% pays 50 every year forever. Compound interest pays 50 in the first year, then 52.50 in the second because the balance is now 1,050, and so on. Over a year or two the difference is small; over thirty it is most of the result.
What is the compound interest formula?
A = P(1 + r/n)^(nt), where P is the starting balance, r is the annual rate as a decimal, n is how many times a year it compounds and t is the number of years. Regular contributions add a second term: the future value of an annuity, c x ((1 + i)^m - 1) / i, where i is the rate per contribution period and m is the number of contributions.
Does compounding more often really make a difference?
Less than most people expect. At 6% over ten years, 10,000 grows to 17,908 compounded yearly and 18,194 compounded monthly, about 1.6% more. Going from monthly to daily adds roughly another 0.1%. The rate and the term matter enormously; the frequency is a detail. Use the effective annual rate shown in the results to compare accounts that compound differently.
What is the effective annual rate?
What a quoted rate actually earns over a year once compounding is taken into account. A 12% rate compounded monthly earns 12.68%, because each month's interest starts earning too. It is the only fair way to compare an account quoting 5.9% compounded daily against one quoting 6% paid yearly.
Are my contributions added before or after interest?
After. Each period the interest is worked out on the balance as it stands, and the contribution is added at the end of the period. This is the ordinary convention for a monthly standing order. Paying in at the start of each period instead would earn one extra period of growth on every contribution, a small difference over a few years and a noticeable one over thirty.
Does this account for tax, fees or inflation?
No, none of the three. Interest may be taxable where you live; funds and platforms charge fees that come straight out of the return; and inflation means the final balance buys less than the same number today. A 1% annual fee against a 6% return removes about a fifth of the growth over a decade. Treat the figure as a gross projection, not as what you will have.
Is this a forecast of what my investment will do?
No. It applies one fixed rate for the whole term. Savings rates change and investment returns vary wildly year to year, a portfolio averaging 7% will have years of +20% and years of -15%, and the order they arrive in changes the result. This is arithmetic on an assumption, which is useful for comparing plans and misleading if read as a prediction.
How long will it take to double my money?
Divide 72 by the interest rate for a quick estimate: at 6%, about 12 years; at 9%, about 8. The rule of 72 is accurate to within a few months for rates between about 4% and 12%. Enter your figures above for the exact answer, and note that the doubling time does not depend on how much you start with.

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