Down 20 per cent, up 20 per cent: why the amount does not return
By Erik Nilsen · Kroni3 min read
A percentage always applies to a particular base amount. Once an amount becomes smaller, a later increase is calculated from the new number. Equal percentage figures therefore do not necessarily cancel each other. Your child can see this with a small practice budget.
Follow one hundred through two changes
In a hypothetical example, a price starts at 100 units. It falls by 20 per cent: 20 per cent of 100 is 20, so the new price is 80. These arbitrary figures describe no actual shop or price trend.
If that 80 then rises by 20 per cent, the addition is 80 × 0.20 = 16 units. The result is 80 + 16 = 96. The price has not returned to 100 despite the percentages matching.
Getting from 80 to 100 requires 20 units. Compare that addition with the current base of 80: 20 / 80 = 0.25, or 25 per cent. A 20 per cent reduction therefore needs a 25 per cent increase to restore this original amount.
Separate amounts from percentages
Write three rows: starting amount 100, after reduction 80, after increase 96. Under the increase write “20 per cent of 80”. That makes it harder to accidentally use the original hundred as the base for the second calculation.
A common snag is your child saying “20 down and 20 up make zero”. That works for money amounts: 100 − 20 + 20 = 100. It does not work for two percentage calculations using different bases. Ask them to explain which operation each row uses.
Also try halving 100 to 50. Increasing 50 by 50 per cent produces 75. Reaching 100 requires doubling 50, which is an increase of 100 per cent. This example makes the principle visible without complicated numbers.
This checks arithmetic rather than predicting that an actual price will return to its previous level. For a purchase, today's confirmed final price must fit your child's available money.
Ask your family: “Which amount represents one hundred per cent before the next change?”
Carry the calculation into your family agreement
Kroni can keep track of your child's virtual balance. The app does not transfer money, so any actual purchase is paid for outside it. Agree on what you will record, then check the amount with your child afterwards. Do not deduct a possible cost as though the purchase had already happened. Read about allowance in Kroni.
