successive percentage increases

[bmwhype]

Price increased by X% from 2001 to 2002 and by Y% from 2002 to 2003.
What is the percentage increase from 2001 to 2003?

1) XY=30
2) 100X+100Y+XY=800

[bmwhype]

Originally Posted by bmwhype

Price increased by X% from 2001 to 2002 and by Y% from 2002 to 2003.
What is the percentage increase from 2001 to 2003?

1) XY=30
2) 100X+100Y+XY=800

Can someone show me how to apply this shortcut? I am not quite understanding it.

here is a short cut formula to remember..

if price is increase by x% then by y% the resulting net increase after the successive increments is always (X + Y + XY/100)

[DWarrior]

Example:
You had $1000
You earned 5% interest the first year
You earned 8% interest the second year

you can do 1000*(1.05)(1.08)=1134

or:
Total increase = 5+8+5*8/100 = 13.4%
1000*(1.134) = 1134

Here's how to derive the shortcut:
A = original
X = first increase %
Y = second increase %

Total increase = A * (100+X)/100 * (100+Y)/100 =
= A * (1+X/100) * (1+Y/100) = A * (1+Y/100+X/100+XY/10000) <- FOIL
Now to convert it back to percents: A * (100+Y+X+XY/100)/100

[bmwhype]

thanks.

how can i rearrange 100X+100Y+XY=800 into that format?

[DWarrior]

Divide through by 100:
X+Y+XY/100=8, meaning the net percent increase will be 8%. We don't actually need to know the individual terms, because we're already given the final sum.

You can also see Statement 1 won't work because we're given XY, but aren't told what X and Y equal, so we can't compute the (X+Y) part (ex: it can be 30*1, X=30 Y=1, or 3*10, X=3 Y=10).

[bmwhype]

Originally Posted by DWarrior

Divide through by 100:
X+Y+XY/100=8, meaning the net percent increase will be 8%. We don't actually need to know the individual terms, because we're already given the final sum.

You can also see Statement 1 won't work because we're given XY, but aren't told what X and Y equal, so we can't compute the (X+Y) part (ex: it can be 30*1, X=30 Y=1, or 3*10, X=3 Y=10).

thanks.

[MBAtoddler]

hey BMW ,

Where did you find that shortcut? Very helpful .

Do u have more of that stuff that you can share?