Question 935624
let x = the amount.
raising it by 25% means that you are adding 25% of x to x.
25% of x is equal to .25 * x.
you get:
x + 25% of x is equal to x + .25 * x which is equal to 1.25 * x.


raising x by 25% of x is the same thing as multiplying x by 1.25.


if you do that 4 times, then you are multiplying x by 1.25 four times.


you get:


x * 1.25 * 1.25 * 1.25 * 1.25


since 1.25 * 1.25 * 1.25 * 1.25 is equal to (1.25)^4, then that expression becomes:


x * 1.25^4


now you have that x * 1.25^4 = 500


divide both sides of this equation by 1.25^4 and you get:


x = 500 / 1.25^4


you can use your calculator to find that x must be equal to 204.8


multiply 204.8 * 1.25^4 and you will get 500


to confirm for yourself that this is the same as 204.8 * 1.25 * 1.25 * 1.25 * 1.25, then do that in your calculator and you will still get 500.