Purpose and steps
For nominal rate a and n compounds per year, effective monthly return = (1 + a / n)^(n / 12) − 1. Grow the balance each month, then add that month’s deposit; increase deposits at each year boundary. The calculation runs locally and keeps cash-flow timing consistent with the stated assumptions.
- Confirm currency and monthly versus annual amounts. U.S. tax and loan models should be used within their stated scope.
- Prepare Starting principal, Nominal annual interest rate, Years, End-of-month contribution, Compounding frequency per year, Annual contribution increase. Defaults demonstrate the model rather than your personal circumstances.
- Check the headline result and its components. A key interpretation for this tool is: APY differs from nominal APR when interest compounds more than once a year.
- Compare the baseline with a changed scenario: The doubling time is for principal alone; additional deposits make the account balance grow differently.
Input reference and units
These values reproduce the model’s demonstration. Replace them with your own records or measurements; they are not recommended targets.
On a small screen, swipe the table horizontally to see all columns.
| Parameter | Demonstration value | How to enter it |
|---|---|---|
| Starting principal | 10000 USD | Use dollars and the monthly or annual period stated in the field label; do not enter thousands of dollars. |
| Nominal annual interest rate | 5 % | Enter a percentage such as 6.5, not 0.065. The equation converts it to a decimal. |
| Years | 10 years | Use years here. The model converts to months when the payment schedule requires it. |
| End-of-month contribution | 100 USD | Use dollars and the monthly or annual period stated in the field label; do not enter thousands of dollars. |
| Compounding frequency per year | 12 times | Use the definition shown in the field label; keep this assumption consistent when comparing scenarios. |
| Annual contribution increase | 0 % | Enter a percentage such as 6.5, not 0.065. The equation converts it to a decimal. |
Model-specific method
How this calculator produces its result
For nominal rate a and n compounds per year, effective monthly return = (1 + a / n)^(n / 12) − 1. Grow the balance each month, then add that month’s deposit; increase deposits at each year boundary.
Geometric growth and a stream of contributions
Compound growth multiplies the previous balance, including earlier interest, by the next period’s growth factor. The contribution term is another geometric sum: the first deposit compounds for longer than the last. It applies only to equal deposits and a constant rate; growing contributions require a different sum or period-by-period simulation.
A nominal rate compounded m times per year has effective annual growth (1+j/m)^m−1. An already effective annual return converts to a monthly rate as (1+g)^(1/12)−1. These are different conventions, so use the one specified by the tool. A constant return model says nothing about volatility or sequence-of-returns risk.
FV = P(1+r)^n FV of end-period deposits = C × ((1+r)^n − 1)/r Beginning-period deposits multiply the deposit term by (1+r)
- P: initial amount
- C: equal contribution per period
- r: growth rate for that period
- n: periods, with contributions and growth on the same schedule
Worked example
With $10,000 initially, 5% nominal interest compounded monthly, and no deposits, one year ends near $10,511.62. Monthly deposits of $100 add $1,200 principal plus their accrued growth.
Reproduce the default scenario
This is a separate example, calculated using the exact engine on the tool page and the defaults in the input reference above. Health examples use metric units. Displayed rounding may differ from intermediate precision.
- Future balance
- 31,998.32 USD
- Total contributions
- 22,000 USD
- Interest earned
- 9,998.32 USD
- Effective annual yield (APY)
- 5.12%
- Principal-only doubling time
- 13.89
Reading results without overstating them
- APY differs from nominal APR when interest compounds more than once a year.
- The doubling time is for principal alone; additional deposits make the account balance grow differently.
Assumptions and exclusions
- Constant rates are hypothetical. Taxes, fees, variable returns and beginning-of-month deposits are excluded. Monthly deposits use an equivalent monthly rate for the selected compounding frequency.
Sources and content notes
Toolify describes the implemented algorithm and its assumptions. Sources below support the topic or applicable rules; they do not endorse this calculator. Examples are illustrative, and published rules take precedence over simplified estimates.
Report a formula, example or translation issue through our contact page. Include the tool name, inputs and expected result so it can be reproduced. Contact Toolify