How compound interest works
With compound interest, the interest you earn is added to your balance, and in the next period interest is calculated on that larger amount. In other words, you earn interest on your interest. With simple interest, every period's interest is calculated on the original principal only. The longer the term, the faster the gap between the two grows.
Balance = principal × (1 + annual rate ÷ n)n × years
Effective annual rate = (1 + annual rate ÷ n)n − 1
Here n is how many times a year interest is added to the balance: 1 for annually, 2 for every six months, 4 for quarterly, 12 for monthly and 365 for daily compounding. Choose the currency of your amounts in the calculator; it only sets the unit and does not convert anything.
Worked example
Suppose you put 10,000 into an account that pays 7% a year and leave it for 10 years:
- Compounded annually: 10,000 × 1.0710 = 19,671.51
- Compounded monthly: 10,000 × (1 + 0.07 ÷ 12)120 ≈ 20,096.61, an effective annual rate of about 7.23%
- Compounded daily: 10,000 × (1 + 0.07 ÷ 365)3,650 ≈ 20,136.18, an effective annual rate of about 7.25%
At the same annual rate, more frequent compounding gives a slightly higher result. The jump from annual to monthly compounding is noticeable; the step from monthly to daily is small. Change the compounding frequency in the calculator to see the difference for your own numbers.
Adding regular contributions
You can enter an amount that is added to the balance at the end of every compounding period. With monthly compounding, the contribution per period is a monthly deposit. Each contribution starts earning interest from the following period. The results table shows the balance for every year, along with the total of your contributions and the total interest, so you can see how much of the growth comes from your own money.
For example, 10,000 plus 100 a month at 7% compounded monthly grows to about 37,405.09 in 10 years. Of that, 22,000 is your own money (10,000 at the start and 120 × 100 in deposits) and about 15,405.09 is interest.
Nominal rate versus effective rate
A 12% nominal annual rate compounded monthly means 1% is applied every month. The effective annual rate measures what twelve months of compounding actually produce together: about 12.68%. With daily compounding the same 12% becomes about 12.75%. When you compare two offers, do not treat one bank's nominal rate and another's effective rate as the same thing. Put them on the same basis first, then compare the effective rates the calculator shows.
Also keep the contribution period in mind: changing the compounding frequency changes the contribution period too. A contribution of 1,000 per month and 1,000 per year are very different savings plans.
A quick check with a 0% rate
Enter a principal of 10,000, a contribution of 100 per period, monthly compounding, a term of 2 years and an interest rate of 0%. The final balance is 10,000 + 24 × 100 = 12,400, and the total interest is zero. Now change only the rate: the total of your contributions stays the same, while the balance and the interest change. This simple check separates the money you put in from the growth the calculation adds.
When contributions are made
This calculator adds each contribution at the end of the period, so the first monthly deposit does not earn interest in its first month. Calculators that add the contribution at the start of each period will therefore show a somewhat higher result for the same inputs. If your deposits are irregular, a single contribution field cannot represent them; track each period's balance separately instead. The table assumes equal, regular contributions.
Reading the yearly table
The year-end balance includes the starting principal, every contribution made up to that point and the interest earned. Total interest is what remains after the principal and contributions are subtracted from the balance. Subtracting one year's balance from the next shows how much the balance grew that year, but not all of that growth is interest: that year's contributions are part of it. For a long-term goal, run the calculation with several different rates. A fixed-rate projection is arithmetic, not a promise that the same rate will be earned in the future.
What the result does not include
- The result is gross nominal growth. Taxes on interest or investment income, account fees and fund costs are not deducted.
- Inflation is not taken into account, so nominal growth is not the same as growth in purchasing power.
- The interest rate is assumed to stay constant for the whole term. Real interest rates and investment returns change over time.
- This page does not recommend any product or provider and is not investment advice.
