Applying multiple percentages at the same time

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kmlawrenson

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If I have a number that is to be simultaneously adjusted by two or more percentages at the same time, how is this calculated?? For example, a store charges two upgrades at the same time at check-out, say 15% more because you are getting a custom finish and 20% more because you are shopping on Tuesday.

Do I take the 15% plus the total to get a new total, and then take 20% plus the new total, for a total of 38% more?? I.E., if x = total before adjustment, then adjusted total = (x) * (1 + 0.15) * (1 + 0.20) = 1.38 * x

Or, do I calculate the total adjustment by splitting the two percentages and applying both to the total before adjustment?? I.E., if x = total before adjustment, then the adjusted total = x + ( x * 0.15) + ( x * 0.20) = 1.35 * x

I am pretty sure the former is correct, but how do I explain this to a colleague??

Thank you for your time, Ken
 
kmlawrenson said:
If I have a number that is to be simultaneously adjusted by two or more percentages at the same time, how is this calculated?? For example, a store charges two upgrades at the same time at check-out, say 15% more because you are getting a custom finish and 20% more because you are shopping on Tuesday.

Do I take the 15% plus the total to get a new total, and then take 20% plus the new total, for a total of 38% more?? I.E., if x = total before adjustment, then adjusted total = (x) * (1 + 0.15) * (1 + 0.20) = 1.38 * x

Or, do I calculate the total adjustment by splitting the two percentages and applying both to the total before adjustment?? I.E., if x = total before adjustment, then the adjusted total = x + ( x * 0.15) + ( x * 0.20) = 1.35 * x

I am pretty sure the former is correct, but how do I explain this to a colleague??

Thank you for your time, Ken
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The first is correct, as the problem is stated. You need to apply one increase after another (logically speaking), though it doesn't matter which order they come in, or if you combine them as you did.

It's conceivable that the store might mean the second, but they would be expected to state that clearly. And if you're the store, you get to decide what you want to do, as long as you communicate it clearly to the customer.

But I'm not going to shop there on Tuesday!
 
How do you explain this to your colleague?
The regular price is $p. Then there is a 15% upgrade bringing the price to 1.15p. Now whatever the price is (and it is $1.15p) since you are shopping on Tuesday you have to pay an additional 20% on the price. So you have to pay 1.2*1.15p = 1.38p.

Are you sure that you do not get a 20% discount on Tuesdays??

I totally agree with Dr Peterson about not shopping there on Tuesdays!
 
I tried to keep the problem generic, with an analogy (the store) that would be easy to digest. In truth, I am trying to explain to counsel why we multiply (i.e. the 1.38 answer) when we are adjusting a tariff rate simultaneously for an annual CPI adjustment and an FTE-based adjustment. He wants to add them...
 
Sometimes a good way to convince a doubter is to use a specific example (of your real situation, not an analogy). Pick a specific set of numbers and show the amount after the correct calculation of the two adjustments; then show what the result would by the additive method; and finally show that the latter result would fall short of the required second adjustment, relative to the result of the first.

For example, using your analogous story, if something originally cost $100, after the first adjustment it is 1.15 * $100 = $115, and after the second, it is 1.20 * $115 = $138. By the additive calculation you get only $135, which is $3 less than the required 20% increase over $115.
 
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