A future balance can grow for two different reasons: you add more money, or the existing balance earns a return. Combining both into one impressive number makes it hard to understand what the model actually assumes. A useful savings projection shows starting capital, additional deposits, and modeled growth separately.
The main Compound Interest Calculator handles one starting balance at a selectable compounding frequency. The monthly savings planner adds a distinct model: monthly compounding and a fixed deposit at the end of each month. Both assume a constant rate and are educational calculations, not forecasts of an investment product.
1. Check a lump-sum baseline first
For one starting amount, the formula is A = P(1 + r/n)^(nt), where r is the annual rate as a decimal and n is compounding periods per year. A starting 10,000 at a nominal 5%, compounded monthly for ten years, grows to approximately 16,470.09. No additional deposits are included in that result.
Changing the starting balance scales this model proportionally. Changing time or rate does not produce a simple linear change, because growth compounds. First run a zero-rate baseline: without interest and without deposits, the starting balance stays unchanged. This helps catch an unexpected field value before evaluating a more complicated scenario.
2. Add deposits at an explicitly stated time
In the monthly planner, each month starts with an existing balance B. Interest is B × annual rate / 1,200. That interest is added, followed by the selected deposit. A deposit made at month-end starts earning modeled interest in the next month, not in the month it was added.
Start with 1,000, a nominal 6% rate, and a 100 monthly deposit. Month one earns 5 in interest and ends at 1,105. Month two earns 5.525 before the next 100 is added, giving 1,210.525 internally. The visible balance rounds to 1,210.53; the following month uses the unrounded balance.
| Month | Opening balance | Interest | Deposit | Closing balance |
|---|---|---|---|---|
| 1 | 1,000 | 5 | 100 | 1,105 |
| 2 | 1,105 | 5.525 | 100 | 1,210.525 |
3. Distinguish the money supplied from modeled growth
After twelve deposits of 100 and an initial 1,000, the total you contributed is 2,200. The difference between the modeled final balance and 2,200 is interest or growth. It is misleading to call the entire ending balance a return on investment because much of it came directly from your own deposits.
The planner displays total deposited and cumulative growth in separate columns. At zero rate the ending balance equals contributions exactly. With a negative constant-rate scenario, modeled growth can be negative even if the balance rises because new deposits exceed the losses. A rising balance alone therefore does not prove a positive return.
4. Avoid double-compounding an effective annual yield
The monthly planner divides a nominal annual rate by twelve. An effective annual yield already includes compounding and is a different input. Entering an effective yield as if it were nominal, then compounding again, overstates the rate relationship. Check the definition used by a bank or financial product before copying a percentage.
The arithmetic relation for a nominal monthly-compounded rate is effective annual rate = (1 + nominal rate / 12)^12 − 1 when rates are expressed as decimals. This relation describes a fixed mathematical rate, not how an investment's variable market returns arrive during a year.
5. Treat the projection as a scenario, not a promise
The planner excludes taxes, account fees, inflation, withdrawals, missed deposits, and changing rates. Those omissions are important. A projected nominal balance does not show future purchasing power, and a constant positive rate is not a guarantee that an investment will avoid losses.
Use a few different rates and deposit amounts to understand sensitivity, keeping the other fields unchanged. Download the monthly CSV to inspect the path, not just the ending balance. The year-end table includes a final partial year when the term is not a whole number of years; every monthly row remains available in the export.
Before using the result
- Identify whether the source rate is nominal or effective.
- Keep lump-sum growth separate from monthly deposits.
- Check deposit timing: this planner adds deposits at month-end.
- Read total contributed and modeled growth independently.
- Consider costs, inflation, and uncertainty outside the calculation.
Try the tools in this guide
- Compound Interest Calculator — Project investment growth with configurable interest and compounding frequency. Open the advanced planner.
- Percentage Calculator — Calculate a percentage of any number with a clear step-by-step result.
Sources and calculation notes
Examples and comparisons are original illustrative calculations, not copied case studies. Reference links explain standards or concepts; they do not endorse this site. See the calculation methodology for engine behavior and precision.
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