How compound interest works
Simple interest pays you only on the amount you started with. Compound interest pays you on the starting amount plus all the interest already earned. Each period, the interest is added to the balance, and the next period’s interest is calculated on that larger number. Over a few months the difference is small, but over decades it becomes the dominant force in long-term saving.
This calculator combines a starting balance with a regular deposit made at the end of every month. You choose the annual rate, the number of years, and how often interest is compounded. The tool converts your chosen frequency into an equivalent monthly growth rate so that monthly deposits can be handled correctly, then steps through every month and records the balance. The yearly table shows how much of the growth came from your own contributions and how much from interest.
The rate you enter is a constant assumption. Real savings accounts change their rates, and investments rise and fall. Use the result as a planning illustration rather than a forecast, and try several rates to see a range of outcomes.
The formula
For a lump sum with no deposits the classic formula is:
A = P × (1 + r / n)n × t
P is the starting amount, r the annual rate as a decimal, n the number of compounding periods per year and t the years. With monthly deposits D added at the end of each month and an effective monthly rate i, the balance after N months is:
A = P × (1 + i)N + D × ((1 + i)N − 1) / i
The first term is the growth of the starting balance, and the second is the growth of the stream of deposits.
Worked example
Start with $10,000, add $200 every month, and assume a steady 7% annual return compounded monthly for 20 years. You contribute $58,000 in total ($10,000 plus 240 deposits of $200). The calculator shows a final balance of $144,573, which means about $86,573 came from interest.
Compare that with doing nothing but leaving the $10,000 alone: it would grow to $40,387. The monthly deposits are what turn a modest start into a much larger sum, and the later years add the most in dollar terms because the balance is largest then.
Tips
- Start early. Time matters more than the size of any single deposit. Ten extra years often beats a higher rate.
- Be conservative with the rate. Run the numbers at a lower return as well as your hopeful one.
- Account for fees and inflation. Fees reduce your effective return, and inflation reduces what the future balance can buy. Subtract both from the rate for a more realistic picture.
- Automate deposits. Consistency is what makes the deposit stream work.
- Remember taxes. Interest and gains may be taxable depending on the account type and where you live.
Frequently asked questions
What is the difference between APR and APY?
APR is the stated yearly rate without counting compounding within the year. APY (or effective annual rate) includes the effect of compounding. At the same APR, more frequent compounding gives a slightly higher APY.
Does compounding frequency matter much?
Less than most people expect. At 5%, annual compounding gives an effective 5.00% while daily compounding gives about 5.13%. The rate and the time horizon matter far more than the frequency.
When are the monthly deposits made?
This calculator assumes each deposit is made at the end of the month, so it earns interest starting the following month. Deposits made at the start of each month would grow slightly more.
Can I use this for investments like stocks?
You can use it as an illustration with an assumed average return, but investment returns are uncertain and uneven from year to year. The result is a projection under a constant-rate assumption, not a prediction.
Why do the last years add the most interest?
Because interest is earned on the whole balance, and the balance is largest at the end. This is the snowball effect that makes long time horizons so powerful.