I NEED $100.00

I have had multiple people ask me lately me lately for assistance calculating a confusing math problem.

They want to get $100 out of an account, but they actually need to withdraw more than that to cover a fee. In reality, this question could be for any amount of money from any source where some additional money is required to cover some sort of penalty or fee or tax on the transaction. For example, the person may wish to withdraw money from an account where 20% of the withdrawal will be withheld for taxes. So if they want $100, how much total do they need to withdraw so that they have $100 in their hand when they walk out the door?

The answer in the above example is $125. But how does one calculate that??

To understand the solution, think of the withdrawal as a pie with equally sized pieces, where the amount withheld is one slice and what you take home are all the other slices. In the above example, since 20% is one part in five, you would cut your imaginary pie into five equally sized pieces. The withheld amount is one slice (20%), and you get to eat the other four (80%)! Since you want $100 worth of pie, your four slices would be worth $25 each. Now, to get the value of the whole pie, you multiply $25 per slice times 5 slices, which comes out to $125.

Now that you get the picture, let’s go back to the math. If 20% is withheld, then you keep 80%. Since 80% is four times 20%, then you know the total amount you need to withdraw is a fourth again as much as you get to keep. Had the withholding been 10%, then you would end up with 90% (so cut your imaginary pie into 10 pieces) and you would need to withdraw one-ninth more than you wanted to keep ($100/9 = $11.11; so withdraw $111.11).