Compound Interest: How to Run the Numbers on Your Own Savings

You've seen the charts: a line that creeps along for years, then shoots up like a hockey stick, with a caption about “the eighth wonder of the world.” Maybe a friend or an ad told you that $200 a month will make you rich. It sounds great, but you have no idea whether the numbers are real, or what they'd look like for your own money.

You don't have to take anyone's word for it. Compound interest is a few lines of arithmetic, and the SEC runs a free calculator you can use to check any claim, including the ones in this article. Here's how the math works and how to run it on your own savings.

Simple interest vs. compound interest

With simple interest, you earn a return only on the money you put in. With compound interest, you also earn a return on your past returns, so each year's growth is a little bigger than the last.

Here's an example using a hypothetical 7% annual return on $10,000, with no money added. This is an assumption for illustration, not a promise. Investments can lose money, and real returns bounce around from year to year.

Year 1: $10,000 × 1.07 = $10,700. You earned $700.
Year 2: $10,700 × 1.07 = $11,449. You earned $749, because the $700 from year one is now earning too.
Year 3: $11,449 × 1.07 = $12,250.43. You earned $801.43.

After 30 years, simple interest would pay $700 a year, for a total of $10,000 + ($700 × 30) = $31,000. Compound growth at the same rate reaches about $76,123. Same money, same rate, same 30 years. The extra $45,000 comes entirely from returns earning returns.

The formula, so you can check any number

The math for a single deposit is:

Future value = starting amount × (1 + annual rate)^years

For the example: $10,000 × 1.07^30. On a phone calculator, type 1.07, raise it to the 30th power (about 7.612), and multiply by 10,000. You get $76,122.55.

The rule of 72: a shortcut for doubling

To estimate how long it takes money to double, divide 72 by the annual rate. The SEC's investor site gives the example that at 9%, money doubles about every 8 years (72 ÷ 9 = 8).

Check it with the formula. At 6%, the rule says 72 ÷ 6 = 12 years. And $10,000 × 1.06^12 = about $20,122. Close enough. The exact answer is about 11.9 years, and the rule is handy precisely because it's quick, not because it's precise.

It also works in reverse, which is useful for debt. A credit card charging 24% doubles an unpaid balance in about three years (72 ÷ 24). That's why paying off high-interest debt in the right order usually comes before investing.

Adding money every month

Most people don't invest a single lump sum. They add a little at a time. Here's another example using a hypothetical 7% return and $200 a month ($2,400 a year), with each year's deposits added at year-end to keep the math simple:

Invest for 30 years: about $226,706. You put in $72,000. The other $154,706 is growth.
Start 10 years later, invest for 20 years: about $98,389. You put in $48,000.

Waiting ten years cost $24,000 in deposits but about $128,000 in ending balance. The early years matter most because that money has the longest to compound.

Run your own numbers on investor.gov

The SEC's Compound Interest Calculator on Investor.gov is free, needs no sign-up, and shows a year-by-year chart. To check the lump-sum example above:

Initial Investment: 10000
Monthly Contribution: 0
Length of Time in Years: 30
Estimated Interest Rate: 7
Interest Rate Variance Range: 0 (or try 2 to see a range from 5% to 9%)
Compound Frequency: Annually

You should see a total of about $76,123. If you do, you've verified the math yourself. Now swap in your own numbers: your current balance, what you can add each month, and a rate you're comfortable assuming.

If you enter the $200 monthly example, expect a result that differs somewhat from the $226,706 above, because the calculator adds deposits monthly instead of once a year. The gap comes from timing, not a mistake, and it's a good reminder that small assumptions shift the output.

To see compounding in your actual accounts, look at your year-end statement. Many brokers show a “change in value” or “investment gain” line separate from “contributions.” On a high-yield savings account, it's the interest-paid line. If that number grows a little faster each year while your deposits stay the same, compounding is doing its job. Check once a year rather than monthly, since short-term market swings will drown it out.

Mistakes that make the projection wrong

Plugging in a rate that's too optimistic. A 10% or 12% assumption over 30 years produces enormous numbers. Use a range with the variance setting, and plan around the lower end.
Forgetting fees. A fund's expense ratio comes straight out of your return. A 7% return with a 1% fee compounds like 6%, and over decades that gap is large. The fee you never see shows the dollar cost.
Ignoring inflation. $226,706 in 30 years won't buy what $226,706 buys today. Running the calculator with a lower rate is a rough way to think in today's dollars.
Mixing up APR and APY on savings. APY already includes compounding; APR doesn't. When comparing savings accounts, compare APY to APY. Why your emergency fund belongs in a high-yield savings account covers what to look for.
Interrupting the compounding. Cashing out early resets the clock. The money you take out stops earning, and so does everything it would have earned.

Any compound interest number you see is only as good as its assumptions. Once you can run the math yourself, you can check those assumptions instead of trusting the chart. If you haven't started yet, investing your first $100 is a good place to begin.