How it works
When deposit and compounding frequencies differ, the equivalent deposit-period rate is (1 + r/n)^(n/m) − 1, or e^(r/m) − 1 for continuous compounding. Growth between deposits uses that same equivalent rate.
FV = P(1 + r/n)^(nt) + Σ(Dk × growth for remaining time). Continuous growth uses e^(rt).
- Enter your initial amount, annual rate and term.
- Choose compounding and a regular deposit frequency.
- Start deposits earn one extra period of interest compared with end deposits.
- Annual increases change later deposits. Inflation divides the balance by (1 + inflation)^years.
- Initial money is included in first-year deposits. A final partial year is shown separately.
Worked example: 100 deposited at each month end, at 6% compounded monthly for 10 years, grows to 16,387.93. Deposits total 12,000.00 and interest is 4,387.93.
Popular results
| Initial amount | Annual interest rate | Term in years | Compounding | Regular deposit | Deposit frequency | Final balance | Total deposits | Total interest earned |
|---|---|---|---|---|---|---|---|---|
| 10,000 | 5% | 10 | Yearly | 0 | None | 16,288.95 | 10,000.00 | 6,288.95 |
| 10,000 | 5% | 10 | Monthly | 0 | None | 16,470.09 | 10,000.00 | 6,470.09 |
| 0 | 6% | 10 | Monthly | 100 | Monthly | 16,387.93 | 12,000.00 | 4,387.93 |
| 5,000 | 7% | 20 | Monthly | 200 | Monthly | 124,379.03 | 53,000.00 | 71,379.03 |
| 1,000 | 3% | 5 | Daily (365) | 0 | None | 1,161.83 | 1,000.00 | 161.83 |
Swipe the table sideways to see the rest.
Things to consider
- Compare start and end deposits.
- Test a lower interest rate as well.
- Check inflation alongside the nominal balance.
- Fees and taxes are not included.
Frequently asked questions
What is compound interest?
Interest earns more interest when it stays in the balance. Regular deposits also earn interest from the time they are added.
What is the compound interest formula?
Without deposits, FV = P(1 + r/n)^(nt). P is the initial amount, r the annual decimal rate, n compounds per year and t years. Add each deposit grown over its remaining time. At 0%, the result is simply all deposits added together.
How does compounding frequency matter?
For the same positive nominal rate, more frequent compounding produces a higher effective annual rate. Daily uses 365 periods per year, and continuous uses exponential growth.
Are start or end deposits better?
A start deposit earns interest for one more deposit period. The amount and number of deposits remain the same.
What is EAR compared with the nominal rate?
The effective annual rate includes compounding: EAR = (1 + r/n)^n − 1. Continuous EAR = e^r − 1. It does not include fees or tax.
What is the Rule of 72?
Divide 72 by the annual percentage rate to estimate doubling time in years without new deposits. It is approximate and is not defined at 0%.
How does inflation affect real returns?
Inflation reduces purchasing power. Divide the projected balance by (1 + inflation rate)^term to express it in today's money. This is not the same as simply subtracting rates.
Are these returns guaranteed?
This is an illustration, not financial advice; returns are not guaranteed and fees and taxes aren't included.
Results are estimates for general information only, not financial, medical or professional advice.