Real return: drag inflation
Drag the solid curve down to raise inflation. The dashed curve is the statement balance at the quoted return. The solid curve is what that balance buys. The default run is 7 percent against 3.2 percent inflation, a real 3.68 percent a year rather than the 3.80 percent subtraction gives.
Real return
3.68%
Subtraction would say
3.80%
Statement $19,672Buying power $14,356Drag the solid curve down to raise inflation.
Illustrative arithmetic on one steady return over 10 years, from $10,000. Not a forecast or advice.
In short
- Drag the solid curve down to raise inflation and open the gap below the statement balance.
- Read the headline: it is the real return from dividing, not from subtracting.
- Push inflation above the quoted return, where the statement still rises and buying power falls.
- Set inflation to zero, where the two curves land on top of each other.
Divide, do not subtract
A real return is . Inflation marks down the gain as well as the original money, so subtraction overstates whenever the return beats prices and understates whenever it trails them.
At 7 percent against 3.2 percent the real rate is 3.68 percent, not 3.80. Over a decade the statement and the buying power separate by a wide gap even though nothing was charged. How real returns work is the identity. Nominal against real return is when to use which figure.
A rising statement can still be a loss
Push inflation above the quoted return. The dashed curve still climbs. The solid curve falls. That is cash in an account paying below inflation: every figure the bank prints is accurate, and the quantity of goods the balance covers is shrinking.
The inflation eroder holds a pile still and drags inflation across it. This picture grows a pile at a quoted return and then takes inflation out. How inflation factors work is the factor on its own, with no return in it.
One side of the ledger
Pick a side and stay on it. Either state a goal in today's money and grow at the real rate, or inflate the goal and grow at the quoted rate. Doing both counts inflation twice. The rate this explorer wants is an effective annual rate. Convert an APR first.
Common questions
Why is subtraction close, and still wrong?
The error is the real return times inflation, over one plus inflation. At low single digits it is a fraction of a point, which is why it survives a glance, and it then compounds along with everything else in a long run.
Which inflation rate is this using?
Whatever you set on the slider, held steady for the years in the picture. A published index wanders. Treat the picture as the arithmetic of one constant pair of rates.
Is the quoted return a forecast?
No. It is a steady rate you set, which is what makes two curves comparable. Real returns arrive unevenly. 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.