# Math Geeks!! Assistance needed!!June 7, 2012 3:48 PM   Subscribe

How should a surcharge be calculated?

This is a real situation (I'm not looking for help with math homework!)

Someone is paying \$1,253 for an insurance policy. He had an accident, and the insurance company adds a 30% surcharge.

The new premium is now \$1,784. By my calculation, that is over 40%. By my numbers, the premium should be \$1,629.
1,253 x 1.3 = 1,629 (simple, no?)

Here is the explanation offered by someone from the company:

Unfortunately, you can't figure out the surcharge amount by adding 30% to the new premium. The only way to figure out the surcharge amount is to take the percentage change between the old premium and the new premium, which Bob mentioned below. You have to back into the number to figure out what was the percentage of the old premium..

\$1253 - \$1784 = \$-531
\$-531 / \$1784 = -29.7% (this is saying there was a 30% decrease in premium between the \$1784 and the \$1253)

So the question is.. what should constitute a 30% surcharge on \$1,253?
posted by elf27 to Work & Money (11 answers total)

Yes, a 30% surcharge would be an additional \$375.90, so you are right.

What is most likely is that the "30% surcharge" is actually a shorthand for something more complex. What does the text of the insurance policy say?
posted by grouse at 3:52 PM on June 7, 2012

You're right. What they've done is equivalent to removing a 30% discount, which is the way I thought no-claims bonuses were usually dealt with... maybe that's what's happening and they're misapplying the word 'surcharge'?
posted by Pre-Taped Call In Show at 3:54 PM on June 7, 2012 [2 favorites]

Yeah, did your insurance documents actually say "We're adding a 30% surcharge onto your rates for an accident"? Is this rate increase occurring starting with the beginning of a new policy period? It's likely that the increase is a surcharge in addition to a normal rate increase.
posted by scarykarrey at 3:55 PM on June 7, 2012

\$1253 x 1.30 = \$1,628.90
\$1,628.90 - \$1253 = \$375.90
posted by Master Gunner at 3:59 PM on June 7, 2012

Yes, calling it a 30% surcharge is faulty terminology. I would have expected the math to work out as you initially did. Same logic as tipping. A 20% tip on a \$10 tab is \$2.00, not \$2.50.

It is, as your math has discovered, a 30% INCREASE, arrived at by taking the original amount and dividing by the reciprocal, if I'm getting my math terms right; 1-x where x is the percentage increase expressed as a decimal: \$1253/(1-.3) = \$1,790 (pretty close - may be \$1784 due to some difference in how it's rounding somewhere)

This is the same calculation one uses when calculating profit. A 20% profit on a \$10 item makes the sale price \$12.50.

But there's nothing to be done; they merely gave a percentage increase as a shorthand for the amount they moved it up, and it is what it is.
posted by randomkeystrike at 4:03 PM on June 7, 2012

They're totally wrong. By their logic, a 100% surcharge would be impossible, unless the service they're providing is free (and would remain free after a 100% surcharge). Take their example:
\$1253 - \$1784 = \$-531
\$-531 / \$1784 = -29.7%
And generalize it:
base - new = difference
difference / new = -surchargePercent
So if the surcharge percentage is 100%, they're saying:
difference / new = -100%*
Which means:
difference + new = 0
But we already know the following:
base - new = difference
Which implies:
base - new + new = difference + new
base = difference + new
base = 0
That is, their logic implies that a 100% surcharge cannot possibly exist, unless the original charge is nothing at all.

Of course, this conclusion that their logic implies is completely absurd. In reality, a 100% surcharge simply means doubling the cost, and there's absolutely nothing impossible about that.

Their base assumption -- "I can calculate a surcharge by calculating backwards from a discount" -- is completely mathematically fallacious.

*: this actually works out to be a division by zero error, but it can be eliminated by considering their method to be "\$-531 = -29.7% * \$1784" instead of "\$-531 / \$1784 = -29.7%".
posted by Flunkie at 4:16 PM on June 7, 2012

Well, to be more clear, "I can calculate a surcharge by calculating backwards from a discount" is actually true, but what they're doing is more specifically "I can calculate a surcharge by calculating backwards from a discount of the percentage that I want the surcharge percentage to be". That more specific thing is simply false.
posted by Flunkie at 4:23 PM on June 7, 2012

Pre-taped has it... What they've done is removed a 30% discount....
So... Was "surcharge" the word they used, in your conversations/contracts/terms?
If so, you maybe (huge maybe) able to get it your way after putting up a huge stink. I doubt it though.
posted by cheemee at 4:50 PM on June 7, 2012

One possibility is the following:

Your friend was previously getting a discount on standard rates. After the accident, he was reverted to standard rates plus a 30% surcharge. Someone at the company tried to explain something they didn't understand.

Otherwise, nthing basically all of the above.
posted by ktkt at 10:49 PM on June 7, 2012

The policy should say how the surcharge is calculated, and the percent amount or dollar amount added. It would be highly unusual for it to be calculated on any basis other than the base rate.
posted by slkinsey at 5:31 AM on June 8, 2012

It would be highly unusual for it to be calculated on any basis other than the base rate.

They are not removing a discount, they are surcharging a base rate. I am going to request a copy of the filing the carrier made with the New York State Insurance Dept. I smell a bureaucratic insurance rat.

Thank you everybody for your responses and support.
posted by elf27 at 6:56 AM on June 8, 2012

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