Principal, contributions, and compound interest
The future balance includes the initial deposit, every monthly contribution and accumulated interest. The chart and table separate deposited amounts from interest and include the final partial year. An optional rate range adds two comparison balances to the result note; the chart and table remain the selected annual-rate scenario.
To compare compounding with interest earned only on the original principal, use the Simple Interest Calculator with the same principal, annual rate, and duration.
The formula
P is the initial deposit, r is the nominal annual rate as a decimal, n is compounding periods per year, and t is years. With monthly deposits, we use an equivalent monthly factor q = (1 + r/n)^(n/12). Each month, the previous balance is multiplied by q, with the contribution added before or after that growth according to your selection. The duration is whole years plus additional months divided by 12. Lower and higher comparisons use the same deposits, duration and timing, with their own constant annual rates.
A single deposit over ten years
An initial deposit of 10,000 at a nominal annual rate of 5%, compounded annually with no additional contributions, grows to 16,288.95 after 10 years. The deposited amount stays 10,000 and the interest earned is 6,288.95.
How to use this calculator
- Enter the initial deposit and monthly contribution.
- Set the annual rate, whole years and 0–11 additional months. The total duration must be 1 month to 100 years.
- Choose a currency label. Advanced options contain compounding frequency, contribution timing and an optional rate range in percentage points.
- Answers update as inputs change. Calculate updates immediately. Inspect the balance, interest, chart and annual/final-period breakdown; a positive rate range adds the lower/higher balances to the answer note.
Why compounding matters
Interest can earn further interest when it stays invested. The longer the balance grows, the larger this effect can become. Regular contributions also increase the base that earns interest.
A fixed rate is useful for comparing scenarios, but market investments do not earn a smooth return. Actual returns can be negative and the sequence of returns affects the result.
Nominal rate versus effective annual rate
The nominal rate is the quoted annual rate before accounting for compounding within the year. At a positive nominal rate, more frequent compounding produces a slightly higher effective annual rate.
For example, 12% nominal interest compounded monthly applies 1% each month. The effective annual growth is (1.01)^12 − 1, or about 12.68%. If your starting rate is already an effective annual rate, choose annual compounding.
Compare rates without assuming a forecast
A range of 2 percentage points around 5% compares constant 3%, 5% and 7% scenarios. It does not apply a different rate in each year or estimate a confidence interval.
Enter only a range that keeps both comparison rates between 0% and 100%. This calculator’s savings model excludes negative rates and withdrawals.
Assumptions & limitations
What this calculation assumes
- Each scenario holds its interest rate and monthly contribution constant.
- Monthly deposits use an equivalent monthly growth factor even when compounding is annual, quarterly, or daily.
- The currency selector labels amounts; it does not convert exchange rates.
- Calculations retain 32 significant digits internally; monetary results are rounded to two decimals.
What to keep in mind
- Taxes, fees, inflation, withdrawals, and variable returns are excluded.
- This is a mathematical scenario, not a prediction or a guaranteed investment return.
- A provider may credit interest differently or use a different day-count convention.
Common questions
What happens if the interest rate is zero?
The future balance equals the initial deposit plus all monthly contributions. There is no interest earned.
Does the timing of contributions matter?
Yes. A contribution at the start of a month receives that month’s growth. An end-of-month contribution begins growing in the next month.
Can I use this for another currency?
Choose one of the currency labels, or treat every amount consistently in your currency. The arithmetic does not depend on currency and no exchange conversion is performed.
Can I calculate fewer than twelve months?
Yes. Enter 0 Whole years and the number of Additional months, from 1 to 11. For eighteen months use 1 year and 6 additional months. The final chart point and table row show the complete chosen period.
Is the rate range a forecast of variable returns?
No. It compares separate constant-rate scenarios. For 5% ± 2 percentage points, the result note shows balances at 3% and 7%; the main answer, chart and table use 5%.
Sources & further reading
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