# I need to know an initial amount. I have the rate and the end amount.

#### nsupanda

##### New member
I profusely apologize if this is posted in the wrong thread, it seems like it would be pre-algebra because it seems like it would be a simple equation (even though I can't figure it out).

This is not a homework problem, but a real-world problem I'm having at work.

I need to know an "initial amount" that is multiplied by a percentage (11.52%) to get an "end amount" of $60,532.61. My boss told me to take$60,532.61 × (1-0.1152) to get the "initial amount" but it just isn't working for me. When I do that, I get $53,559.25. And when I take$53,559.25 + ($53,559.25 × 0.1152) I end up getting$59,729.28, which is NOT $60,532.61. What am I doing wrong? #### HallsofIvy ##### Elite Member You say the amount is "multiplied" by the percentage but if that were the case the result would be much less than the amount. It looks to me like you intend that the amount be increased by that percentage: R= A+AP= A(1+ P) so that A= R/(1+ P). Instead of multiplying by 1- 0.1152 you should be dividing by 1+ 0.1152.$60,532.61/1.1152= $54,279.60. #### Dr.Peterson ##### Elite Member I profusely apologize if this is posted in the wrong thread, it seems like it would be pre-algebra because it seems like it would be a simple equation (even though I can't figure it out). This is not a homework problem, but a real-world problem I'm having at work. I need to know an "initial amount" that is multiplied by a percentage (11.52%) to get an "end amount" of$60,532.61.

My boss told me to take $60,532.61 × (1-0.1152) to get the "initial amount" but it just isn't working for me. When I do that, I get$53,559.25. And when I take $53,559.25 + ($53,559.25 × 0.1152) I end up getting $59,729.28, which is NOT$60,532.61.

What am I doing wrong?
It's great that you checked your answer as you did. Often a failed check can be turned into a successful equation!

Replacing the answer you are checking with the variable x, the check, $53,559.25 + ($53,559.25 * 0.1152) =? $60,532.61, becomes the equation x + (x * 0.1152) = 60,532.61. To solve this equation, combine like terms on the left to get 1.1152x = 60,532.61, and solve by dividing: x = 60,532.61/1.1152 = 54,279.60. What your boss is doing is reducing$60,532.61 by 11.52%, which is not the same as undoing an increase by 11.52%, because he is taking 11.52% of the resulting amount rather of the initial amount. That is a common mistake. You are wise to have checked the answer.