See what a balance grows into
Set a starting sum, what you add each month, a rate and a term. The projected balance redraws as you change any of them.
How it works
Interest paid on interest already paid is the entire mechanism, and it takes an uncomfortably long time to look like anything. On the figures this page opens with, year one earns 919 dollars and year twenty earns 20,061. Same rate, same deposit, twenty-one times the return, because by the end the balance doing the earning is around thirty times the size it started at.
The crossover, and why it arrives so late
In any long plan there is a year when the interest earned so far passes the money paid in so far. With ten thousand to start, five hundred a month and seven percent, it lands in year seventeen of twenty. Everything before that point is mostly your own money stacking up. Everything after it is the account out-earning you. Cutting the term short does not move the crossover nearer; it deletes the part of the plan that sits beyond it.
Compounding frequency matters less than the rate
Daily compounding gets advertised and is a small effect. Hold that same plan and switch from annual to daily compounding and the projection moves from 284,670 to 301,613, near enough six percent. Going from monthly to daily is worth 763 dollars out of three hundred thousand. A rate a quarter of a point higher beats any change of frequency. The effective annual rate beside the answer is the honest comparison: 7 percent nominal is 7.0000 percent compounded annually against 7.2501 percent compounded daily.
Start of the period or end of it
A deposit made on the first of the month earns that month. One made on the last day does not. Across twenty years of five hundred a month at seven percent, that single period of offset comes to 1,519 dollars, and most calculators never state which convention they picked. The two have names: an annuity due pays at the start, an ordinary annuity at the end. You can choose here. The default is the end, being the cautious reading, and the gap between them is printed under the answer.
Where this will disagree with a statement
Three places. A bank credits interest in whole pennies every period while this rounds once at the finish, so a thousand pounds at five percent for ten years reads 1,628.89 here and 1,628.91 in an account that rounded up ten times along the way. Tax on the interest is not modelled and in most countries it is real. And money paid in between two compounding dates starts earning on the later one, matching a savings account, though a fund accruing daily will edge ahead of that.
Questions
Why does my provider quote a different number?
Usually one of four reasons: they credit interest to the penny each period and this rounds at the end, their year is 360 days rather than 365, they applied a bonus rate for the first twelve months, or they are quoting the effective annual rate where you entered a nominal one. Setting compounding to annually and entering the AER makes the two agree.
What rate should I use for a stock market return?
Long-run global equity returns are often modelled around 7 percent nominal before costs, or nearer 5 percent after inflation. Real returns arrive in a scattered order rather than evenly, so a projection like this describes an average path and not the one you will get. Subtract your platform and fund fees from the rate before entering it.
Is the effective annual rate the same as APY?
Yes. APY in the United States, AER in the United Kingdom, and effective annual rate in a textbook all mean the figure a nominal rate actually earns once its compounding frequency is counted. Five percent compounded monthly is 5.1162 percent; compounded daily it is 5.1267 percent. Comparing two accounts on that number is the only fair comparison.
What is in the CSV?
One row per year with the opening balance, what you paid in that year, the interest credited, and the closing balance. The columns add up across each row, so a spreadsheet can chart the balance or check the arithmetic without any further work.