Compound interest means you earn interest on your interest. In the first few years the effect is small; over a few decades it can add up to more than everything you put in. Running your own numbers makes it easier to set a monthly savings target and to see what an extra five or ten years of saving is worth.
How the compound interest formula works
Compound interest applies the rate to your starting balance and to the interest already earned. The calculator first converts the annual rate r and the number of compounding periods per year k into an equivalent monthly rate i, so that monthly deposits and any compounding schedule line up.
It then grows the balance one month at a time and adds your contribution at the end of each month. The formula's first part, P(1 + i)^(12t), is what your starting balance P becomes after t years; the second part is the future value of the monthly deposits PMT. Because each month starts from a slightly larger balance, growth speeds up the longer the money stays invested.
Worked example: growing a $10,000 balance
For example, start with $10,000 and add $400 at the end of every month. At a 7% annual rate compounded monthly, the balance after 25 years is $381,282.86. Your $10,000 start plus $120,000 in monthly contributions accounts for $130,000 of that; the other $251,282.86 is interest. Monthly compounding turns the 7% nominal rate into an effective annual rate (APY) of about 7.23%.
Drop the monthly contributions and the same $10,000 grows to $57,254.18. Keep the $400 a month but compound once a year instead of monthly, and the balance comes to $367,491.08, which is $13,791.78 less over 25 years.
What moves your balance the most
Time does most of the work. In the example above, interest earned over the first 10 years totals $31,330.54; by year 20 it is $142,758.05, and the last five years alone add about $108,525. Contributions come next: without the $400 a month, the result is less than a sixth as large. The rate is the input you control least, so it is worth testing a conservative figure alongside an optimistic one. For a full plan with an employer match and a withdrawal rate, try the retirement calculator.
Limits and assumptions
This projection assumes a completely fixed annual rate of return and steady contributions, which real financial markets rarely deliver. It does not account for the impact of inflation, taxes on your gains, or investment account fees. Real returns vary from year to year and are not guaranteed. Treat the result as an educational illustration of how compounding works over a long timeline, not a strict promise of future performance.
Key terms
- Principal
- The original sum of money you start with before any interest is added or new contributions are made.
- Compound interest
- Interest calculated on the initial principal and also on the accumulated interest from previous periods.
- Compounding frequency
- How often the earned interest is applied to the account balance, such as daily, monthly, or annually.
- Monthly contribution
- A recurring deposit made into the account at the end of each month to build the balance.
- Effective annual rate
- The yearly rate once compounding is included, also called APY. A 7% rate compounded monthly works out to about 7.23% a year.