What does compound interest turn my money into?

Interest is credited a set number of times a year, and each crediting is applied to the balance the last one left behind. The calculator turns your annual rate into an effective monthly growth factor, m = (1 + rate / compounds) ^ (compounds / 12) - 1, then walks the balance forward one month at a time: multiply by (1 + m), then add the monthly contribution at the end of the month. With monthly crediting, m is exactly the annual rate divided by twelve.

Written as one expression for a lump sum, that is the compound interest formula every textbook prints: A = P(1 + r/n) ^ (nt). A is the ending balance, P the starting amount, r the annual rate as a decimal, n the number of times a year interest is credited, and t the years. The m above is the same formula cut into months: raising (1 + r/n) to the power n / 12 is one month of growth, and applying that 12t times applies (1 + r/n) nt times, which is the closed form again. The walk exists so a monthly contribution has somewhere to land. Switch the contribution off and the two agree: $10,000 at 7% credited 12 times a year for 20 years is $40,387 by the formula and $40,387 by the month-by-month walk.

Crediting more often makes the same nominal rate yield slightly more over a year. That effective annual yield is (1 + rate / compounds) ^ compounds - 1; at the default 7% compounded monthly it is 7.23%. The frequency control under the result prices yearly, monthly, and daily crediting for your inputs, and the gap is always smaller than people expect.

The one number the model cannot supply is the rate. It is an assumption you choose, not a statistic this page can cite, because no published average promises anything about the account or investment your money actually sits in. Everything downstream, the final balance, the doubling time, the growth share, moves with that choice, which is why the drivers list prices a single point of rate for your exact inputs.

Simple interest pays the rate on the original principal and on nothing else. Interest is credited, and then it sits there: it never earns. The balance is a straight line, P(1 + rt), rising by the same $700 every year at $10,000 and 7%, in year 40 exactly as in year one. Compound interest pays the rate on the principal plus every dollar of interest already credited, which is how the SEC investor glossary defines it: interest paid on principal and on accumulated interest. That single difference in the crediting rule is the whole of this calculator.

Here is what the difference is worth, with the monthly contribution switched off so nothing but the rule changes. Both columns start from $10,000 at an assumed 7%.

The difference column is not a markup that scales with time; it is the distance between adding and multiplying. Simple interest adds $700 in year 40, the same amount it added in year one. Compounding charges the rate on the balance it has already built, so year 40 alone adds $10,997. That is why the two lines are nearly indistinguishable early, $676 apart at 5 years, and unrecognizable late, $125,114 apart at 40. Interest compounds whenever it is credited to the balance and left there, which is what a savings account, a reinvested dividend, and an untouched fund position all do. The straight line is on this page as the counterfactual, not as an option on the form.

At the default inputs, $10,000 to start plus $250 a month at an assumed 7% grows to $170,619 in 20 years. You put in $70,000 of that; compounding adds $100,619, which is 59% of the final balance. Here is the same plan across assumed rates and horizons.

Read the table down a column and across a row. Down a column, each point of rate widens the gap because growth compounds on growth. Across a row, the third decade adds more than the first two: at 7%, the plan reaches $63,368 in ten years but $386,158 in thirty. Time in the plan is the input you control most reliably, which is exactly why the honest move is to be conservative about the one you control least, the rate.

The rule of 72 says money doubles in about 72 divided by the rate. It is a mental shortcut, and this page computes both it and the exact answer so you can see the gap. At the default 7%, the rule gives 10.3 years; the exact figure with monthly compounding, ln(2) divided by twelve times ln(1 + m), is 9.9 years.

The gap moves with the rate. At 4% the rule says 18.0 years against an exact 17.4; at 10% it says 7.2 against 7.0. With monthly compounding the exact time runs a little under the rule at every rate here, because crediting twelve times a year beats the annual crediting the rule quietly assumes. The arithmetic section under the result reports the exact doubling time for whatever rate and frequency you enter.

Doubling time describes an untouched balance. Your contributions make the account cross double the starting amount far sooner, but that is deposits doing the work, not compounding; the composition bar under the result keeps the two honest.

Taxes. Interest, dividends, and realized gains are taxed differently in a brokerage account, an IRA, and a 401(k), and the model compounds the gross rate as if none of it were taxed along the way. In a taxable account the after-tax outcome is lower than the number above.

Fees and inflation. An expense ratio or advisory fee comes straight out of the return before compounding does its work, so enter a rate net of the fees you actually pay if you want the balance in real hands. And the result is in future dollars; inflation decides what those dollars buy, and the model does not touch it.

Sequence of returns. The model applies the same rate every month. Real investments do not: two decades that average the same rate can end in different places once contributions are involved, because it matters whether the bad years come early or late. A steady-rate model is the right tool for understanding compounding and the wrong one for promising an outcome.

This calculator is built to be used without a browser. Every input is a query parameter on this page, and the same parameters on the JSON twin return the complete answer as a document.

GET /tools/compound-interest.json?principal=50000&rate=7&years=30

The response carries inputs after parsing and clamping, result with the final balance, the contribution and growth split, the effective annual yield, the exact doubling time, and yearly rows of contributed, growth, and balance, plus sensitivity tables by rate and by years, drivers ranked by effect with a plain sentence each, assumptions that say for every field whether you supplied it and name the source when the default came from one, sources with a URL and an as-of date for each source the tool cites, which is an empty list on the calculators whose every default is an example input rather than a published figure, warnings, a disclaimer, and in tool the canonicalUrl and jsonUrl that carry only your non-default parameters. The canonical URL is the answer's permanent address; use it when you cite the number.

Parameters, all optional, in any order:

• principal ($), default $10,000.
• monthly ($ per month), default $250 per month.
• rate (%), default 7%.
• years (years), default 20 years.
• compounds (count), default 12.

Values accept plain numbers and loose human formats such as 100k, $100,000, or 6.5%. Unknown parameters are ignored, values outside a field's range are clamped and reported in warnings, and the endpoint never fails on bad input. Responses are cacheable for a day; the defaults change when their sources publish, and tool.version changes when the method does.

No input on this page carries a source, on purpose. Every default is an example input: the rate is an assumption you choose rather than a statistic anyone publishes about your money, and the starting amount, contribution, and horizon are placeholders to replace with your own. The arithmetic itself is the standard compound-growth recurrence stated in the methodology above, and its closed form, A = P(1 + r/n) ^ (nt), is the textbook one.

The single outside reference on the page is definitional. The SEC investor glossary defines compound interest as interest paid on principal and on accumulated interest, which is exactly the rule the recurrence implements and exactly what separates it from the simple interest line above.

Carlo is a personal finance agent. It knows your accounts, debts, and goals, so instead of an example account at an assumed rate it can tell you what your actual saving rate is compounding toward, and what changing it would do to the goals you are funding. Text it the question.

ask carlo anything(415) 376-5678