What compound interest is
With simple interest you earn interest only on the money you put in. With compound interest, interest that has been added to the account earns interest too. The effect is small in the first years and grows faster over time, which is why starting early matters more than almost anything else in long-term saving.
Future value of a lump sum = P × (1 + r ÷ k)^(k × t)
P = starting amount, r = annual rate, k = compounding periods per year, t = years
For regular monthly deposits D (with monthly compounding), the deposits grow as an annuity:
Future value of deposits = D × ((1 + r ÷ 12)^(12t) − 1) ÷ (r ÷ 12)
The calculator handles other compounding frequencies by converting the rate to an equivalent rate per month.
Worked example
10,000 at 5% a year, compounded monthly, for 10 years:
10,000 × (1 + 0.05 ÷ 12)^120 = 16,470.09
Adding 200 a month for the same 10 years adds 200 × ((1.0041667)^120 − 1) ÷ 0.0041667 = 31,056.46. Total: 47,526.55, from deposits of 34,000. The other 13,526.55 is interest.
How often interest is compounded
| Compounding of 10,000 at 5% for 10 years | Final amount |
|---|---|
| Yearly | 16,288.95 |
| Monthly | 16,470.09 |
| Daily | 16,486.65 |
More frequent compounding helps a little, but the rate and the time invested matter far more. This is also why banks quote an APY or AER (annual equivalent rate): it shows the yearly return after compounding, so accounts with different compounding can be compared fairly. 5% compounded monthly is an APY of about 5.12%.
The rule of 72
A quick way to estimate how long money takes to double: divide 72 by the annual rate. At 6%, money doubles in about 72 ÷ 6 = 12 years (the exact answer is 11.9). At 3% it takes about 24 years; at 9%, about 8.
What the calculator does not include
- Inflation: a 5% return with 3% inflation is roughly a 2% gain in purchasing power.
- Taxes and fees: both reduce the real growth of savings and investments.
- Variable returns: investments such as shares do not grow at a steady rate. A fixed rate is only an average assumption, and real results can be lower or higher, including losses.
Common mistakes
- Confusing the interest rate with APY. Compare savings accounts by APY/AER.
- Expecting straight-line growth. Most of the gain from compounding appears in the later years.
- Treating projections as guarantees. Use several rates (for example 3%, 5% and 7%) to see a range.
For education only; not financial advice.
How time and rate change the result
10,000 invested with monthly compounding and no further deposits grows to:
| Annual rate | After 10 years | After 20 years | After 30 years |
|---|---|---|---|
| 3% | 13,494 | 18,208 | 24,568 |
| 5% | 16,470 | 27,126 | 44,677 |
| 7% | 20,097 | 40,387 | 81,165 |
Doubling the time more than doubles the gain, and at 7% the amount roughly doubles every ten years. This is the core reason to start saving early.
Adjusting for inflation
To see what a future amount is worth in today's money, divide by (1 + inflation)years. 16,470 after ten years with 3% yearly inflation is worth about 16,470 ÷ 1.0310 ≈ 12,255 in today's terms. Your real (after-inflation) return is roughly the interest rate minus the inflation rate.
Compound interest on debt
The same maths works against you on credit cards and loans: unpaid interest is added to the balance and then charged interest itself. Paying off high-interest debt is often the best "return" available, because every unit repaid stops compounding at that high rate.
Frequently asked questions
How do I calculate compound interest?
Use A = P × (1 + r ÷ k)^(k × t). For 10,000 at 5% compounded monthly for 10 years: 10,000 × (1 + 0.05/12)^120 = 16,470.09.
What is the difference between simple and compound interest?
Simple interest is paid only on the original amount. Compound interest is also paid on interest already earned, so growth speeds up over time.
Does daily compounding make a big difference?
Not much compared with monthly: 16,486.65 versus 16,470.09 in the example. The interest rate and time matter far more.
What is the rule of 72?
Divide 72 by the annual interest rate to estimate the years needed to double your money. At 6%, about 12 years.
How much will 10,000 grow in 20 years at 5%?
About 27,126 with monthly compounding and no further deposits.
How do I account for inflation?
Divide the future amount by (1 + inflation rate) to the power of the number of years to express it in today's money.
Does compound interest apply to debt?
Yes. Unpaid interest on credit cards and many loans is added to the balance and itself earns interest for the lender.
Sources
- US Securities and Exchange Commission, Investor.gov: Compound interest calculator and explanation.
- UK Financial Conduct Authority: AER (annual equivalent rate) definition for savings products.
Last reviewed 5 October 2026. Results are estimates; see our disclaimer.