How to use the calculator
- Enter what you start with, the annual interest rate and how many years the money stays invested.
- Choose how often interest is compounded. Savings accounts usually compound daily or monthly, many bonds twice a year, and a quoted "annual return" on investments is effectively yearly.
- Add a monthly contribution if you will keep saving, and say whether it goes in at the start or the end of each month.
- Read the final balance, how much of it you contributed and how much is interest. The chart shows the balance at the end of each year, with the interest part in green; the table below lists the same figures.
The compound interest formula
With a nominal annual rate r compounded n times a year for t years, a starting amount P grows to:
A = P × (1 + r/n)^(n × t)The more often interest is compounded, the sooner each slice of interest starts earning interest of its own, so the balance grows slightly faster. The effective annual rate captures this: (1 + r/n)^n − 1. A nominal 5% compounded monthly is an effective 5.116% a year; compounded daily it is 5.127%. When comparing savings accounts, compare these effective rates — in the US they are published as the APY.
Regular contributions
Monthly contributions form an annuity. When each payment C goes in at the end of the month and the monthly growth rate is i, the contributions alone grow to:
FV = C × ((1 + i)^m − 1) / iwhere m is the number of months. Paying in at the start of each month gives every payment one extra month of growth, which multiplies the result by (1 + i). The calculator simulates the account month by month, converting the chosen compounding frequency into an equivalent monthly rate, so it handles combinations such as monthly contributions with quarterly compounding correctly. Figures are rounded to the cent only for display.
The rule of 72
A quick mental shortcut: money doubles in roughly 72 ÷ rate years. At 5%, that is 14.4 years; the exact figure for yearly compounding is ln 2 ÷ ln 1.05 = 14.2 years, which is what the calculator shows as time to double.
Worked examples
| Scenario | Result after 10 years |
|---|---|
| $10,000 at 5%, compounded yearly | $16,288.95 |
| $10,000 at 5%, compounded quarterly | $16,436.19 |
| $10,000 at 5%, compounded monthly | $16,470.09 |
| $10,000 at 5%, compounded daily | $16,486.65 |
| $100 a month at 6%, paid at month end | $16,387.93 (you paid in $12,000) |
| $100 a month at 6%, paid at month start | $16,469.87 |
Starting with $10,000 and adding $200 a month for 20 years at 7%, compounded monthly, you pay in $58,000 in total. The account ends at $144,572.72, so $86,572.72 — more than you contributed — is interest. Most of it arrives in the last years: that is compounding at work, and why starting early matters more than contributing a lot later.
At 0% interest the calculator simply adds up what you put in: $5,000 plus $100 a month for three years is $8,600.
Limits
- Fixed rate. Real savings rates change and investment returns vary from year to year; a steady average rate overstates how smooth the path will be and says nothing about the risk of losses.
- No inflation, tax or fees. A 7% return with 3% inflation grows purchasing power by about 4% a year. Taxes on interest and fund fees reduce the result further.
- Monthly contributions only. Yearly lump sums or irregular deposits can be approximated by changing the starting amount and running the calculator in stages.
- Not financial advice. Use the figures to compare scenarios, not as a forecast of what an investment will return.
Frequently asked questions
What is compound interest?
Interest that is added to the balance and then earns interest itself. Over long periods it makes growth accelerate, because each year's interest is calculated on a larger balance.
Does compounding frequency matter much?
A little. $10,000 at 5% for 10 years ends at $16,288.95 with yearly compounding and $16,486.65 with daily compounding — about 1.2% more.
What is the difference between APR and APY?
APR is the nominal yearly rate; APY (the effective annual rate) includes the effect of compounding within the year. For savings, compare APY.
Should contributions be at the start or end of the month?
Contributions at the start of the month earn one month more interest each, so the final balance is slightly higher. Use whichever matches when your deposits actually happen.
Are my numbers saved?
No. The calculation runs in your browser, and nothing is stored or sent.