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Overstatement of the naive sum
The exact amount by which adding the rates overshoots. For 0.20 and 0.10 it is 0.02, printed as 0.020000000000000018.
The Formula
Overstated = (a + b) - (a + b - a x b) = a x b
The exact amount by which adding the rates overshoots. For 0.20 and 0.10 it is 0.02, printed as 0.020000000000000018.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| a | First discount as a decimal | decimal | 0.20 in the worked example. |
| b | Second discount as a decimal | decimal | 0.10 in the worked example, giving a product of 0.02. |
| delta | Overstatement | decimal | The product of the two rates, always positive, equal to 0.020000000000000018 here. |
What Each Symbol Means
adecimal
First discount as a decimal
0.20 in the worked example.
bdecimal
Second discount as a decimal
0.10 in the worked example, giving a product of 0.02.
deltadecimal
Overstatement
The product of the two rates, always positive, equal to 0.020000000000000018 here.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate stacked discounts page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Stacked Discounts, filed under Everyday Life. Every number the guide produces comes from substituting into this one line.