How Compound Interest Works, With Real Numbers
By Akmal Ali · Published · Updated · 5 min read
Compound interest adds each period’s interest to the balance, so later interest is earned on a larger amount. The formula is A = P(1 + r/n)^(nt), and regular deposits grow the same way: saving 200 a month for 10 years at 6% compounded monthly gives 32,775.87, of which 8,775.87 is interest.
Compound interest is interest on interest. Each time interest is added to a balance, the next interest payment is calculated on the larger amount, so growth speeds up the longer the money stays in. Over a few years the effect is small; over a working life it is most of the result.
The four inputs
- Principal (P): the amount you start with.
- Interest rate (r): the yearly rate as a decimal. 5% is 0.05.
- Compounding frequency (n): how many times a year interest is added. Annually is 1, quarterly 4, monthly 12, daily usually 365.
- Time (t): the number of years.
The compound interest formula
A = P × (1 + r ÷ n)n × t
A is the final amount. The interest earned is A − P. In words: divide the yearly rate by the number of periods in a year, add 1, raise it to the total number of periods, and multiply by the starting amount.
Worked example: 10,000 at 5% for 10 years
With interest compounded once a year, n = 1:
- Rate per period: 0.05 ÷ 1 = 0.05, so the growth factor is 1.05.
- Number of periods: 1 × 10 = 10.
- 1.0510 = 1.628895.
- A = 10,000 × 1.628895 = 16,288.95.
The interest earned is 16,288.95 − 10,000 = 6,288.95. Year by year, the balance grows to 10,500, then 11,025, then 11,576.25: each year’s 5% is calculated on a bigger number than the last.
Compound Interest Calculator
Choose the compounding frequency, add optional monthly deposits, and see the balance year by year.
How does compounding frequency change the result?
The same 10,000 at 5% for 10 years, compounded more often:
| Compounding | n | Final amount | Interest |
|---|---|---|---|
| Annually | 1 | 16,288.95 | 6,288.95 |
| Semi-annually | 2 | 16,386.16 | 6,386.16 |
| Quarterly | 4 | 16,436.19 | 6,436.19 |
| Monthly | 12 | 16,470.09 | 6,470.09 |
| Daily | 365 | 16,486.65 | 6,486.65 |
More frequent compounding helps, but with diminishing returns: going from annual to monthly adds about 181, and from monthly to daily only about 17 more. The rate and the time matter far more than the frequency.
This is also why savings accounts quote an effective annual rate (called APY or AER in some countries). 5% compounded monthly is the same as 5.116% compounded once a year:
effective annual rate = (1 + r ÷ n)n − 1
Simple vs compound interest
Simple interest is paid only on the original amount: A = P × (1 + r × t). The difference is small at first and grows every year:
| After | Simple interest | Compound (annual) | Difference |
|---|---|---|---|
| 1 year | 10,500.00 | 10,500.00 | 0.00 |
| 5 years | 12,500.00 | 12,762.82 | 262.82 |
| 10 years | 15,000.00 | 16,288.95 | 1,288.95 |
| 20 years | 20,000.00 | 26,532.98 | 6,532.98 |
| 30 years | 25,000.00 | 43,219.42 | 18,219.42 |
After 30 years, compounding has earned 33,219.42 in interest against 15,000 for simple interest, more than twice as much, at the same rate. The simple interest calculator shows both figures side by side for your own numbers.
Adding regular deposits
Most savings grow from regular deposits as well as a starting amount. Saving 200 at the end of every month for 10 years at 6% compounded monthly gives 32,775.87: 24,000 of your own deposits plus 8,775.87 in interest. Start with 5,000 as well, and the total after 10 years is 41,872.85. The compound interest calculator handles deposits for any compounding frequency.
How long does it take to double your money?
The rule of 72 is a quick estimate: divide 72 by the yearly interest rate in percent. At 6%, money doubles in about 72 ÷ 6 = 12 years (the exact answer with annual compounding is 11.9). At 5% it gives 14.4 years, against an exact 14.2. It’s an approximation, most accurate for rates between about 5% and 10%.
In a spreadsheet
Excel, Google Sheets and LibreOffice calculate the final amount with the FV function:
=FV(5%/12, 12*10, 0, -10000)The arguments are the rate per period, the number of periods, the regular payment (0 here) and the starting amount as a negative number. This returns 16,470.09, the monthly-compounding result from the table.
Does compounding work on debt too?
Unpaid interest on a credit card or loan can be added to the balance, and then charged interest itself. The same maths that grows savings makes an unpaid debt grow. Paying off high-interest debt is often worth more than the interest you’d earn by saving the same money. For loans repaid in fixed monthly instalments, see how to calculate EMI.
What does the formula leave out?
The formula assumes a fixed rate for the whole period and no fees, taxes or withdrawals. Real savings rates change, investments can lose value, and inflation reduces what the final amount will buy. Use these calculations to understand and compare options, not as a promise of returns. They aren’t financial advice.
Frequently Asked Questions
What is continuous compounding?
It is the limit of compounding more and more often, calculated as A = P × e^(r × t). For 10,000 at 5% for 10 years it gives 16,487.21, only 0.56 more than compounding daily, so in practice daily and continuous compounding are almost the same.
How does inflation change what my money is worth?
Divide the final amount by (1 + inflation rate) raised to the number of years. 16,288.95 after 10 years at 5% is worth about 12,120.51 in today’s money if prices rise 3% a year, a real return of about 1.94% a year.
How much do I need to invest now to reach a target?
Divide the target by the growth factor: P = A ÷ (1 + r ÷ n)^(n × t). To have 20,000 in 10 years at 5% compounded yearly, you need 20,000 ÷ 1.05¹⁰ = 20,000 ÷ 1.6288946 = 12,278.27 today.