Compare the following sentences:

1) You received a raise and your income increased to 135% of its previous amount.

2) You received a raise and your income increased by 135%

Answer: Let us assume that our income is $X.

In the first case:

1) We received a raise and our income increased to 135% of its previous amount.

"increased to" denotes that we will multiply our original income by the percentage given.

Therefore our income would be = $X * 1.35 = $1.35

X

In the second case:

2) We received a raise and our income increased by 135%.

"increased by" denotes that we have to add the given percentage of our income to our original income.

Therefore our income would be $X + $X*1.35 = $2.35X