Compound interest: formula, monthly deposits, and assumptions
Compound interest means interest can earn additional interest over time. Your result depends on the starting balance, the stated annual rate, how often interest compounds, the time invested, and any recurring deposits. This calculator assumes the selected rate stays constant for the entire period; it is a mathematical scenario, not a prediction of investment returns.
Formula for a starting balance
A = P × (1 + r/n)nt, where P is the starting deposit, r is the annual rate expressed as a decimal, n is the number of compounding periods per year, and t is the number of years. With monthly contributions, the calculator adds each month’s deposit at month-end and applies a monthly growth rate equivalent to the selected annual compounding assumption.
Worked example
A $5,000 starting deposit at a constant 7% annual rate, compounded monthly for 20 years with no added deposits, grows to approximately $20,193.69 before taxes, fees, and inflation. The difference from the original $5,000 is estimated interest, not guaranteed profit.
How to interpret the result
- Amount invested is the starting deposit plus the monthly contributions you entered.
- Interest earned is the modeled future value minus those contributions.
- Higher rates or longer time periods can increase the projection, but actual savings and investment returns can vary; fees, taxes, inflation, and market losses are not modeled here.
For another explanation of compound growth and its inputs, see the U.S. Securities and Exchange Commission’s Investor.gov Compound Interest Calculator.
Tips for accurate results
Enter the rate as the annual percentage and choose the compounding schedule that matches the account. If you make regular deposits, enter them consistently and decide whether they happen at the start or end of each period, as that changes the outcome slightly. Try a lower rate than the one you hope for to see a more cautious scenario.
Common mistakes and limits
The calculation assumes a constant rate, which real investments rarely deliver. Inflation reduces purchasing power, and taxes and fees reduce what you keep, none of which are in the base result. Use the projection to compare plans, not to predict a specific balance.
Learn more: How compound interest works, with worked examples.