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(male narrator) So suppose a stock drops in value by 60% one week
and then increases in value the next week by 75%.
Is the value higher or lower than when it started?
So this is, uh...an issue of combining percents,
and it's really tempting to say,
oh, it drops by 60%, increases by 75%.
It must be 15% up.
Unfortunately, that's not the way percents work,
because the base changes in each case.
So let's start and imagine that our...
the value of our stock starts at $100.
So at the end of the first week, the-the value drops by 60%.
So we could either say, I have my 100%,
and I decrease by 60% of my 100.
Or in other words, I drop by $60, gives me $40.
Or alternatively, we could've said
that decreasing by 60% is the same as keeping 40%.
So we could've said, $100--I'm keeping 40%.
Get to the same thing, but either way works.
So here we go.
At...we...after... the first week,
the value has dropped by $60, by 60%,
and we're left with $40 in value.
So the next week, the value is gonna increase by 75%,
but the base has changed.
We're now increasing by 75%--
not of the original hundred, but of the new value.
And because the base has changed,
the result is gonna change.
So 75% of $40 is only $30.
So it turns out after two weeks,
the value of my stock is only $70.
It is, in fact, 30% lower...
than where it started.
Okay, and this is really important
when you are shopping, for example.
And, uh...you know, you see the-the items
that are, you know, on clearance for 50%,
and then the sign says,
"And this week, take an additional 50% off."
Well, that doesn't mean you get it for free, right?
'Cause they take the first 50%, and then you...
the second discount is 50% of that sale price.
You end up paying a quarter.
Uh...you don't get it for free.
So that's an important thing to remember--
that the base changes when you combine percents.