Compound Interest Calculator

How this is calculated

The future value is the starting amount multiplied by (1 + rate / 100 / periods) raised to the power of periods x years. The division by 100 is written into the formula on purpose: the rate is entered as a PERCENTAGE, so 7 has to become 0.07 before it goes anywhere near the exponent. Reading the formula with 7 in it rather than 0.07 produces nonsense, which is why it is spelled out rather than mentioned afterwards. Simple interest is shown alongside for contrast: starting amount x (1 + rate / 100 x years), where the interest is calculated only on the original sum and never on itself. The gap between the two columns is the entire point of compounding, and over long periods it becomes most of the answer rather than a detail. Compounding frequency matters far less than people expect. Going from annual to monthly on a 7 percent rate over 20 years adds a few percent to the total; going from 20 years to 25 adds far more. Frequency is a rounding detail next to time and rate, and a product advertising daily compounding is not offering you much over one that compounds monthly. The doubling time is worked out properly with logarithms: the natural log of 2, divided by the periods per year times the natural log of (1 + rate / 100 / periods). The familiar Rule of 72 - divide 72 by the rate to get the doubling years - is an approximation of that, and a good one in the middle of the range. It drifts at the extremes, reading a little short at low rates and a little long at high ones. This models a LUMP SUM left alone. It does not handle regular contributions - for that, the savings goal calculator solves the related question of what you need to add each month to reach a target. Everything here is nominal and before tax and inflation, which is a large omission over long periods. A 7 percent return with 3 percent inflation is roughly 4 percent in purchasing power, and forty years of that difference is not a detail. Interest is usually taxable too unless the account is sheltered.

Common questions

Why show simple interest as well?

Because the gap between the two columns IS compound interest, and it is far more legible than the total on its own. At 7 percent over 20 years, ten thousand becomes about forty thousand compounded and twenty-four thousand simple - so more than a third of the final figure is interest that was itself earning interest. Quoted as a total, that is just a big number; quoted as a difference, it is the argument for starting early.

Does compounding frequency matter much?

Much less than people expect. On a 7 percent rate over 20 years, moving from annual to monthly compounding adds only a few percent to the total, and monthly to daily adds almost nothing on top - the returns flatten out fast. Time and rate dominate completely. A product advertising daily compounding is not offering you a meaningfully different deal from one compounding monthly, and it is not worth choosing on.

How good is the Rule of 72?

Good in the middle and loose at the edges. Dividing 72 by your interest rate gives an approximate doubling time, and it is remarkably close for rates roughly between 5 and 12 percent. It drifts outside that range - reading a little short at very low rates and a little long at very high ones. The calculator does it properly with logarithms, so you can see the size of the gap for your own numbers.

What about my monthly contributions?

Not modelled here - this is a lump sum left alone, which keeps the compounding effect visible rather than tangled up with new money going in. For regular contributions, the savings goal calculator answers the related question of what you need to add each month to reach a target by a date, including the interest earned along the way.

Is this before or after inflation?

Before, and over long periods that is a large omission rather than a technicality. A 7 percent nominal return with 3 percent inflation is roughly 4 percent in real purchasing power, and compounding that difference over decades produces a very different picture. If you want the answer in today's money, enter the real rate - your expected return minus expected inflation - instead of the nominal one.

What rate should I use?

Whatever you can actually justify, and lower rather than higher if you are unsure. Compounding amplifies optimism as ruthlessly as it amplifies returns: over 30 years, assuming 10 percent instead of 7 roughly doubles the projected total, which makes a plan built on the higher figure fail quietly and late. Savings accounts pay their stated APY; investment returns are not a rate you get to choose.

Take it further with AI

Copy this into ChatGPT or Claude with your own numbers filled in. It hands over the figures this calculator worked out, so the answer is built on real arithmetic instead of a guess.

I used the Compound Interest Calculator at https://www.bfcbrilliance.com/tools/compound-interest-calculator.

What I entered:
- Starting amount ($): ___
- Annual rate (%): ___
- Left for (years): ___
- Compounded: ___

What it calculated:
- Grows to: ___
- Interest earned: ___
- Same money at SIMPLE interest: ___
- What compounding added: ___
- Years to double: ___

Use those figures as given — they are already worked out, so please don't recalculate or estimate your own. Help me turn them into a plan: what to buy or do, in what order, roughly what it should cost, and the mistakes people most often make with this job.

Keep this general and do not give financial advice — flag where I should talk to a qualified adviser.

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