Compound growth curve you can drag
Drag the curve up for a higher annual return and down for a lower one. The dashed line is the money paid in, so the shaded gap is the compounding. The default run is an illustrative 20 years at 7 percent a year, ending near 2.4 times the amount paid in.
Annual return
7.0%
Balance after 20 years
$196,665
BalanceMoney paid inDrag the curve up for a higher return, down for a lower one.
The top of the frame is the balance the fastest return here would reach, so the picture holds still while you drag. Every figure is illustrative arithmetic on the settings you pick, held at one steady rate, and not a forecast or advice.
In short
- Drag the curve up to raise the annual return, down to lower it.
- Watch the shaded gap: that part of the balance is interest, not money you paid in.
- Pull the years slider out to 40 to see how late most of the growth arrives.
- Set the return to zero, where the balance line lands exactly on the paid-in line and the gap closes.
Why the curve bends
A straight line adds the same amount every year. A compounding balance adds a percentage of a balance that keeps getting bigger, so each year's gain is larger than the one before it and the line pulls away from the dashed line underneath.
At a zero return there is nothing to compound and the two lines sit on top of each other. Every bit of daylight between them is interest, and it arrives in two parts: interest on the money you paid in, and interest on interest already earned. On the default run the second part is a little under half of the gap, and by 40 years it passes seven tenths, because it is the part that needs time.
Why the last years do the most work
Hold the return at 7 percent and drag the years slider from 20 to 40. The money paid in comes up short of double, because the fixed starting amount does not double when the months do. The ending balance grows by nearly five times.
Read both from the numbers above the chart. The frame is redrawn for every run, which is why its top carries a label. That gap between not quite double and nearly five times is the argument for starting early. At any return above zero the steepest stretch of the curve is the one on the right, and it only exists because the years in front of it happened first.
What each slider changes
The starting amount does more than lift the picture. It compounds on its own, so it raises the balance line a little on the left and much more on the right, while it lifts the dashed line by the same flat amount the whole way across. Widening that daylight is what a head start buys.
The monthly amount steepens the dashed line as well as the balance line, because it is money paid in rather than money earned. Years does not stretch the picture sideways: the run always fills the width, so a longer one draws more years into the same space and rescales the height with them.
For the same arithmetic as a table of numbers instead of a shape, use the compound interest calculator.
Common questions
How often does this compound?
Interest is added monthly, and the monthly amount is paid at the end of each month, which is the convention a payroll deduction or a standing order follows. The curve itself is drawn from one sample a year.
Why does the balance line sit on the dashed line at a zero return?
Because at a zero return the balance is only the money you paid in. Height above the dashed line is the interest, so at zero there is nothing to draw above it. The line still climbs, because the monthly amount keeps arriving.
Is the annual return meant to be a forecast?
No. It is a steady rate you set yourself, which is what makes two shapes comparable, and no rate on the slider is a prediction about any investment. Real returns arrive unevenly, so read the curve as the arithmetic of one constant rate over the years you picked. It is educational material, not advice.
Keep reading
This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.