As we saw in a previous post, adding a percentage is a multiplication.

For instance, adding 20% to a tax free price, to obtain the VAT included price, is multiplying by (1+20/100)=1.20=1.2.

But what I would like you to know today, is that subtracting a percentage is NOT a division, but a multiplication as well!

For instance, a coupon of 30% on a price of $100 is subtracting 30% of $100, that is (30/10)*$100=$30. The reduced price is $100-$30=$70, that is 0.70 times $100.

Another way to see it is that to subtract 30%, we have to multiply by 30/100=0.3 and then to subtract the result os the multiplication by 0.3 to the intial amount. Thus, we multiply the intial amount by (1-30/100)=0.70=0.7.

Now, let's combine the 2 operations.

Suppose that you have invested an amount of $1,000 and are rewarded by 10%: you get $1,100 back, and you earned $100.

Suppose now you leave the $1,100 to wait a better earning, but you loose the same 10%: you loose $1,100*(10/100)=$110, so that you get $1,100-$110=$990.

Thus the result of a gain of 10% and then a loss of 10% (add and subtract 10%) is a loss of $10, that is 1% of $1,000.

You may see then that add and subtract a given percentage are NOT reciprocal operations. This is because they are both multiplications, as the reciprocal operation of a multiplication is a division.

In any case, this is a confirmation that when you invest on the financial market, you haven't earned anything until you get your money back!