ABC Tools

Compound Interest, Explained

After reading this you will be able to project how a starting balance plus monthly deposits grow over time, compute the result by hand for any compounding frequency, and read the split between your money and the interest it earns.

What compound interest is

Compound interest means the interest you earn is added to the balance, and then that larger balance earns interest too. The interest earns interest. Over short periods the effect is small. Over decades it dominates.

Here is one number to fix the idea. Put 10000 in an account paying 7% per year, compounded monthly, add nothing more, and wait 10 years. The balance is 20097. Your money roughly doubled without a single extra deposit. The extra 10097 is interest, and much of it is interest paid on earlier interest.

This calculator goes one step further: it also lets you add a fixed amount every month, which is how most people actually save. The result combines two growth engines: the lump sum compounding on its own, and each contribution compounding from the month it arrives.

When to use it, and when not

Use this tool when you have a starting balance, a steady monthly deposit, and a fixed assumed rate, and you want to see the balance at the end. Retirement accounts, index-fund savings plans, and long-run savings goals all fit this shape.

Do not use it when the rate is not fixed or the contribution is not level. Real investment returns swing from year to year. A 7% average return does not mean 7% every year, and the order of good and bad years changes the outcome when you are withdrawing. This calculator assumes one constant rate, so treat its output as a smooth central estimate, not a forecast.

A single assumed rate hides real risk. If you enter 7%, the tool shows one clean curve, but a portfolio that averages 7% can spend years below and above that line. Use the number to compare plans, not to predict a specific balance on a specific date.

The formula and the intuition

Two pieces add together. The first is the lump sum. A principal P at annual rate r, compounded m times per year for t years, grows to:

FV_{\text{lump}} = P \left(1 + \frac{r}{m}\right)^{m t}

Here r is written as a decimal, so 7% is 0.07. The rate per period is r/m, and there are m t periods. Each period multiplies the balance by (1 + r/m), so applying it m t times gives the exponent.

The second piece is the stream of contributions. This tool assumes a deposit C at the end of every month, so there are 12 t deposits. Each one compounds for the months remaining after it arrives. Summing that geometric series gives the future value of an ordinary annuity:

FV_{\text{contrib}} = C \cdot \frac{(1 + i)^{n} - 1}{i}

Here n = 12 t is the number of deposits and i is the interest rate over one month. When the account compounds monthly, i = r/12 directly. When it compounds at some other frequency, the monthly growth factor is (1 + r/m)^{m/12}, so i = (1 + r/m)^{m/12} - 1. The total is FV_{\text{lump}} + FV_{\text{contrib}}.

A worked example with the demo numbers

10000 start, 100 per month, 7% for 10 years

These are the tool's default values: principal = 10000, rate = 7%, years = 10, monthly compounding (m = 12), and contribution = 100.

  1. Monthly rate: i = 0.07 / 12 = 0.005833.
  2. Number of periods: n = 12 \times 10 = 120.
  3. Growth factor: (1 + 0.005833)^{120} = 2.0097.
  4. Lump sum: 10000 \times 2.0097 = 20097.
  5. Contributions: 100 \times \frac{2.0097 - 1}{0.005833} = 100 \times 173.08 = 17308.
  6. Total: 20097 + 17308 = 37405.

Of the ending 37405, you deposited 10000 at the start plus 120 × 100 = 12000 in contributions, so 22000 is your own money. The remaining 15405 is interest. Interest is 41% of the final balance after only 10 years, and that share keeps climbing the longer you leave it.

Watching the split grow

The chart below tracks the same plan year by year and shows how the gap between total balance and money paid in widens. Early on the two lines sit close together. By year 10 the interest wedge is clearly visible.

The lower series is your own money. The gap to the upper series is accumulated interest, which grows faster each year.

An interactive view of frequency and rate

Compounding frequency matters less than people expect, and rate matters far more. The widget lets you move both and watch the ending balance react, holding the demo's other inputs fixed.

With principal 10000, 100 per month, and 10 years fixed: at 7% the ending balance is about 37405 with monthly compounding and 37421 with daily compounding, a difference of only 16 dollars. Raising the rate to 9% lifts the monthly result to about 42163, and dropping to 5% lowers it to about 33269. Rate moves the answer by thousands; frequency moves it by tens.

Reading and interpreting the results

The tool gives you three things: an ending balance, a growth chart, and a year-by-year table splitting each year into contributions and interest. Read them in this order.

Start with the ending balance, then subtract what you put in. In the demo that is 37405 - 22000 = 15405 of interest. That difference is the whole point of compounding, so look at it directly rather than at the headline balance alone.

Next, scan the table for the year where annual interest first exceeds your annual contributions. Your yearly contribution is 1200. Interest passes that mark partway through the plan, and once it does, your balance grows faster from interest than from your own deposits. That crossover is the moment compounding takes over.

To compare two plans fairly, keep years and contributions equal and change only the rate. If you want to solve for the rate or the term instead of the balance, the Time Value of Money Solver rearranges the same equation for any single unknown.

Common mistakes

Confusing nominal rate with effective rate
A 7% nominal rate compounded monthly earns an effective annual rate of (1 + 0.07/12)^{12} - 1 = 7.23\%. If you compare two accounts quoted at different frequencies, convert both to effective terms first with the APY / Effective Rate Calculator.
Entering the rate as a decimal in a percent field
Typing 0.07 where the field expects 7 gives a rate of 0.07% and a nearly flat curve. Enter percentages as whole numbers.
Ignoring inflation
The 37405 is in future dollars. If prices rise 3% a year for 10 years, those dollars buy what about 27834 buys today. The tool projects nominal balances, not purchasing power.
Assuming the average return happens every year
A constant 7% is a modeling convenience. Real returns vary, and this matters most when you withdraw. Treat the smooth curve as a midpoint.

Related tools

Once you understand the balance projection, these tools answer the neighboring questions. To find the monthly deposit that hits a target amount by a set date, use the Savings Goal Calculator. To see how long a fixed balance lasts once you start spending it, use the Savings Withdrawal Calculator, and to find when your savings reach a milestone like a million, try the Savings Milestone Calculator.

For a fixed-term deposit with no monthly contributions, the Deposit / CD Calculator is a closer match. To see how much compounding actually adds, compare against the Simple Interest Calculator. For quick doubling estimates use the Rule of 72 Calculator, and to see the limit as compounding frequency rises without bound, the Continuous Compounding Calculator shows the P e^{r t} case.

Frequently asked questions

Does more frequent compounding really matter?

Barely, at ordinary rates. In the demo, monthly compounding gives 37405 and daily gives about 37421, a difference of 16 dollars over 10 years. Annual compounding gives about 37243. The rate and the time horizon dwarf the frequency.

Why are contributions assumed to arrive at the end of the month?

This tool uses an ordinary annuity, where each deposit lands at the end of its month and so earns nothing that month. If deposits arrived at the start of each month instead, each would earn one extra month of interest, raising the demo total by roughly 0.583% of the contribution part, about 100 dollars.

Is the ending balance guaranteed?

No. It is guaranteed only if the rate is truly fixed, as with a bond held to maturity or a CD. For investments with variable returns, the number is a central estimate that assumes the average holds every year.

How do I account for taxes and fees?

Subtract them from the rate. If you expect 7% but pay 0.5% in fund fees and lose 1% to tax on the growth, model it by entering a lower net rate such as 5.5%. The tool has no separate fee field.

Try it yourself in the tool

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