What compound interest is
Compound interest is interest earned on interest. Each period, the return is added to the balance, so the next period's return is calculated on a bigger number. Early on the growth looks linear; over decades the curve bends upwards, and time in the market matters more than the exact rate.
The formula
For a single deposit, the balance after t years is P × (1 + r/n)n·t, where P is the starting amount, r the annual rate and n how many times a year interest is added. 10,000 at 7% compounded annually for 20 years becomes about 38,700.
How this calculator works
Monthly contributions are added at the end of each month. The rate you choose is converted to the equivalent monthly rate for your compounding frequency, so a contribution starts earning from the following month. The range applies your variance below and above the estimate, never going under 0%.
What it leaves out
Real returns are not smooth: markets fall, sometimes for years. The projection also ignores taxes, inflation and fees beyond what you take off the rate yourself. Use it to compare plans, not to predict a number.