Percentage
When thinking it terms of percentages, be wary of if a total is being added to, or reduced from. If the total is being added to, then the percentage we add to the total gives us the cumulative return of the whole new total. However, if we are subtracting a percentage from the total, then the amount of the % return is actually a number higher than the one the total was reduced by.
- ex. When putting money into an RESP, the government matches 20%. We are adding to a total. $1000 + 20% is $1200. In a way, 20% return right off the bat. Straightforward. But imagine we are talking about a discount. For instance, buying shares in your company through an ESPP gives you a 15% discount, this does not mean that we are getting a 15% return right off the bat. Here, we are reducing from a total. If we were buying $1000 worth of shares without ESPP, the cost of those shares with ESPP would be $850. Since we can go ahead and sell those shares on the open market immediately for $1000, we have made a return of $150 over the $850 investment:
( 1000-850 ) / 850 = 17.6%.
Mental trick: Figuring out percentages of complex numbers
if you ever have to calculate a difficult percentage on the spot without pen and paper or a calculator, you can use a simple shortcut - flip the numbers around.
- ex. if you needed to work out 4% of 75 in your head, just flip it and do 75% of 4, which is easier
This basic principle – simply stated as "x as a percentage of y = y as a percentage of x"
- this trick works simply because of the fact that (known as Commutative Laws)