How to use the compound interest calculator
Start with the amount you already have, then add the money you expect to contribute each month. These are separate inputs: the initial balance is deposited once, while monthly contributions continue throughout the selected period.
- Enter your starting balance and monthly contribution. Use US dollars consistently. Set the monthly contribution to zero to model a single deposit.
- Choose the annual rate and rate type. Select a nominal annual rate or an effective annual rate, depending on the figure you have.
- Set the time horizon and compounding frequency. Daily, monthly, quarterly, and annual compounding describe how frequently interest is added to the balance.
- Choose when contributions arrive. Beginning-of-month deposits earn interest for one additional month compared with otherwise identical end-of-month deposits.
- Add an inflation assumption if needed. This provides a separate estimate of future purchasing power; it does not reduce the displayed account balance.
For a useful comparison, change one input at a time. This makes it easier to distinguish the effect of a larger contribution from the effect of a longer saving period.
Annual rates, APY, and compounding frequency
A nominal annual rate states the rate before the effect of compounding within the year. An effective annual rate includes that effect. For a constant nominal rate r compounded n times per year, the effective annual rate is (1 + r/n)^n − 1. Rates in this formula are decimals.
For example, an illustrative 6% nominal annual rate compounded monthly produces an effective annual rate of approximately 6.1678%. Entering 6% as an effective rate describes a different scenario from entering 6% as a nominal rate.
At the same positive nominal rate, more frequent compounding increases the effective annual yield: daily exceeds monthly, monthly exceeds quarterly, and quarterly exceeds annual. If the effective annual rate is held constant, changing the frequency does not create an additional annual return on a single untouched deposit.
APY describes an annual yield that incorporates compounding. For this calculator's nominal/APR setting, use the annual rate before compounding. A loan's disclosed APR can include borrowing costs, so it is not automatically a suitable savings input.
How monthly contributions enter the formula
For one initial deposit without contributions, the standard formula is:
A = P × (1 + r/n)^(n × t)
Here, A is the future balance, P is the starting principal, r is the nominal annual rate, n is the number of compounding periods per year, and t is time in years.
A monthly compound interest calculator must also account for when each contribution enters the balance. With monthly compounding and equal deposits at the end of each month, the formula becomes:
A = P × (1 + i)^m + C × ((1 + i)^m − 1) / i
In this formula, i = r/12, m is the total number of months, and C is the monthly contribution. For beginning-of-month deposits, multiply only the contribution term by (1 + i). At a zero rate, use A = P + C × m.
The second formula applies directly when both contributions and compounding are monthly. Other frequencies require a consistent conversion between interest periods and contribution timing; dividing an effective annual rate by 12 is not the correct monthly conversion.
Example: $10,000 plus $500 per month
Assume an initial balance of $10,000, contributions of $500 at the end of every month, a constant 6% nominal annual rate compounded monthly, and a 10-year period. These figures illustrate the calculation and do not represent an available account or an expected investment return.
| Result | Amount |
|---|---|
| Initial balance | $10,000.00 |
| Monthly contributions over 120 months | $60,000.00 |
| Total money contributed | $70,000.00 |
| Interest earned | $30,133.64 |
| Future balance | $100,133.64 |
The calculation uses a monthly rate of 0.5%, retains precision during the calculation, and rounds the displayed results to cents. Moving all contributions to the beginning of each month increases the final balance to $100,543.34 under the same assumptions.
How to interpret the result
The future balance combines your own money with accumulated interest. Total contributions include both the initial deposit and subsequent monthly deposits. Interest earned is the difference between the future balance and that total; a larger balance does not mean the entire increase came from returns.
The inflation-adjusted amount expresses the ending balance in today's dollars. With constant annual inflation f, it is A / (1 + f)^t. In the example, an illustrative 2.5% annual inflation assumption gives purchasing power of approximately $78,224.24. This is an adjusted value of the final balance, not a measure of real investment profit.
Assumptions and related calculations
The model holds the selected rate constant and assumes interest stays invested. Taxes and fees are excluded. Actual accounts may use different crediting dates, day-count rules, or rounding, while investment returns can vary and include losses. This investment compound interest calculator models the rate you enter; its result is not personalized financial advice.
Use the daily compound interest calculator for actual dates and day-count conventions, or the compound interest calculator with withdrawals for regular spending from a balance. The continuous compound interest calculator uses a continuous growth model. To solve for an unknown amount, rate, or duration without contributions, use the compound interest formula calculator.
Adjust your contribution, rate, or time horizon above to compare another scenario.