Piecewise Function: Project

Let$$s look at $3$ scenarios.

You will calculate the tax for each scenario to see how this works.

Scenario $1$: Your father bought stock in Amazon in the year $2000.$ He bought $500$ shares. The

stock was worth $$0\mathrm{.}78$ per share so he spent $500*0\mathrm{.}78,$ or $$390.$ He sold it on July $2021$ and on

that day, that same stock was worth $$186\mathrm{.}57$ per share. So$,$ his $500$ shares were now worth

$500*186\mathrm{.}57,$ or $$93,285.$ His total capital gain is $$93,285-$$$390=$$$92,895.$ He has a job where his

income is $$50,000.$ His total taxable income is $$92,895+$ $$50,000=$ $$142,895.$

Scenario $2$: Your Mother has been working for $15$ years as a soldier and her wage income for a

year is $$92,895.$ She sold some mutual funds this year and had a capital gain of $$50,000.$ Her

total taxable income is $$142,895.$

Scenario $3$: You bought a run$-$down rental property. You paid $$400,000,$ you spent $$107,105$ in

renovations, and then quickly sold the house for $$600,000.$ You would have a capital gain, which

comes from taking $$600,000$ minus the $$107,105$ you spent in renovations minus the $$400,000$

you paid for the property, or $600,000-$ $$107,105-400,000,$ or $$92,895.$ You work as a Part Time

IT guy as your part$-$time job and make $$50,000$ in wage income. Your total taxable income is

$$142,895.$

Note in all $3$ scenarios, everybody ended up with taxable income of $$142,895.$

They should all owe the same amount on taxes, right?

Nope. Not even close. Since scenario $1$ and $3$ have capital gain of $$92,895$and wages of $$50,000,$

they are calculated differently than if you had wage income of $$92,895$ and capital gains of

$$50,000.$

Scenario $1$ Solution: Capital gains are taxed at $15\%($this is true unless your wage income starts

to get high and then this can go up to $20\%$ and for some certain items like selling a piece of art,

you might pay $28\%).$

You take $15\%$ of $$$92,895.$ This is $0\mathrm{.}15*$$$92,895,$ or $$13,934\mathrm{.}25.$ Then we will figure income tax

on $$50,000.$ This is the $3$rd bracket. You substitute $40,000$ in your $3$rd piece of the piecewise

function. It is $4543+0\mathrm{.}22*(50,00039475)=$ $$6858\mathrm{.}50.$

You sum the two amounts of tax: capital gains tax of $$13,934\mathrm{.}25$ and income tax of $$6858\mathrm{.}50$

and you get $$20792\mathrm{.}75.$

Let$$s calculate the effective tax rate. You take tax paid divided by taxable income...

$$20792\mathrm{.}75/$$$142,895,$ or $14\mathrm{.}55\%.$

Piecewise Function: Project

QUESTIONS:

$11)$ Calculate the two taxes, capital gains and income tax based on scenario $2.$

$12)$ What is the total tax due? Find the effective tax rate

$13)$ What is the difference in total tax dollar amounts between scenario $1$ and scenario $2?$