Here’s an income tax problem. We’re given a tax
table and were asked to find how much someone who is married and filing
separately from their spouse will owe on a taxable income of \$98,400. The first step with a
problem like this where we have taxable income and we want to find the tax that’s owed
is to split up the income into these different tax brackets. Now again, the way
this works is you can pretend that you have a number of barrels (as poorly drawn as
these are, let’s pretend they’re barrels). Into each of these barrels you put some
money. Now the first barrel corresponds to the 10 percent bracket, the second barrel
corresponds to the 15 percent bracket, the third to the 25 percent bracket, the fourth to the
28 percent bracket, and so on–as many barrels as you need. And then above these barrels you
line up all of your money, from dollar number one all the way up 2 dollar number 98,400. If you split these up, the first \$9075, everything from dollar number 1
through dollar number 9075 goes in the first barrel. Then the next dollars all the way up to dollar number
36,900 go into the second barrel, everything from that point on to dollar number
74,425 go into the third barrel and so on. So each dollar only goes into one barrel and
these brackets split up your money and divide it up as far as how much gets taxed
from each group. So for instance, for this person, the amount that would go into the 10
percent bracket is the 9,075. To find how much goes into the 15 percent bracket, we need to subtract 36,900 minus 9075, and this
will give us how many of their dollars fit into this bracket. The difference
between those is 27,825 so \$27,825 go into the 15% bracket. We do the
same with the next two brackets; so for instance, for the 25 percent
bracket we subtract 74,425 minus 36,900 to find out
how many dollars go in that second bracket. In this case, we find that that’s
37,525, so into the third bracket we put \$37,525. And then we have the fourth
bracket, the 28 percent bracket: again here we’re putting the rest of our money in here. Notice that with a taxable income of \$98,400 we
don’t spill over into the fifth bracket. We have dollars number 74,425 up through 98,400 – those are the only remaining ones. So to find how
many go in the fourth bracket we take our final amount minus 74,425. If we
had more than \$113,425 we would fill up this whole
barrel and spill over into the next one. But for now, since we stopped at \$98,400, we subtract
these and get \$23,975. So in the fourth bracket, we have \$23,975; the next step is
to figure out how much gets taxed from each bracket. Now, in the first bracket there’s
\$9075 and 10% of that gets taxed, so we calculate
10% of \$9075 which is \$907.50. Similarly, 15% of \$27,825 is \$4173.75 and 25% of \$37,525 is \$9381.25, and 28% of \$23,975 is \$6713 even. So
this is how much gets taxed from each bracket, and the total tax that’s owed is the sum of
these four numbers–the sum of these four taxed amounts–so our final step is
to add these four together. Adding them up, we get a total of \$21,175.50 so that is the final tax
owed. There are a lot of steps in this process but it all boils down to putting the taxable
income into these different brackets, figuring out how much goes into each
bracket, and then taking that appropriate percentage of the amount in that bracket
and adding up all those taxes owed.