% of a % convention

Factual Questions
1

My job involves looking at various car loan and lease rates, and I noticed a convention that I’m not sure applies generally to mathematics.
Sometimes a loan program will have a discounted rate if certain criteria are met - i.e., a 6.25% rate will be reduced by .25%. Inevitably, the intent is a resulting rate of 6.00%.

But I have a feeling that if I asked somebody, without context, “What is 6.25% reduced by .25%” the answer would be 6.234375% (i.e., 6.25*.9975).

Or maybe to use a real life example, if I said that, due to new data, the chance of rain predicted this morning at 50% just went up by 20%, would you understand there was a 70% or a 60% chance of rain?

Is there a convention in math that dictates how to interpret x% +/- x%?

Maybe this belongs in IMHO, not sure…figured I’d try here first.

–KidScruffy

2

If it’s not in the context of a math class, I infer that the examples you’ve cited are implied to be added, not multiplied.

But that’s just me. I think the implied wording, and most people understand it as such is "by 0.25 percentage points.

And so far as GQ, your question as phrased answers itself. You just use +/-. It keeps things simple.

3

x% +/- y% is properly equal to x% +/- (x * y)/100
If you want the (x +/- y)% answer, y should be measured in percentage points rather than %.

In everyday language though you never know what is meant. Percentage points is a good bet in both your examples, but the second one could be refering to an actual 20% increase.

4

Thanks for the answers - I wasn’t familiar with using the phrase “percentage points” as a unit of measure, but that would certaintly clarify things. Presumably there’s no symbol or shorthand for “percentage point” as a unit of measure, since % is already taken…?

5

It’s all good, as long as you are sure to explicitly state what you are taking a percent of. Normally, you don’t need this, it’s usually clear from context. But in your case, there are two valid interpretations, you just need to state which one is being used.

6

Another way of avoiding the confusion is the term “basis points.” One basis point is 1/100 of a percent point, or 0.01%. So if I told you “we’ll take 25 basis points off your 6.25% interest rate” then that means your rate is 6.00%. This term is primarily used in the finance industry, where it’s obviously very useful.