Some proposals for replacing the Affordable Care Act ("Obamacare") rely on an existing mechanism called health flexible spending accounts (FSA’s). At the beginning of the year, you decide how much money to put in an FSA. This money is deducted from your wages before taxes, thus reducing your tax payments. However, if you do not use all the money in the FSA by the end of the year, it reverts to your employer.
A person who earns between $39,746 and $84,200 per year after deductions is in the 29.65% federal tax bracket (7.65% for Social Security and Medicare, plus 22% for income taxes). Suppose such a person believes that their out-of-pocket health care expenses are equally like to be $1000, $1500, $2000, $2500, $3000, $3500, $4000, or $4500 in the coming year.
1. To maximize the expected benefit from their FSA, how much should they contribute to it?

Assume that you are choosing to put $1000 in your FSA account,  

The addition from this is you can get the duty derivations on $1000 which is equivalent to the ($1000 × 29.65%) = $296.5  

In the event that you increment a dollar in the FSA record and you can spend it, at that point you get the advantage of sum you spared from charge derivation,  

Reasoning in charge in the event that you store $1001 in FSA account = $1001 × 29.65%  

Reasoning in charge in the event that you store $1001 in FSA account = $296.8  

Net advantage of contributing one additional dollar in FSA when you spend,(G) = Deduction in charge by contributing $1001 - reasoning in charge by contributing $1000  

= $296.8 - 296.5  

= 0.3  

Assume you are not ready to spend an additional dollar you contribute on FSA account, so the net advantages will diminish by $1, (L) = 0.3 - 1 = - 0.7  

On the off chance that he contributing $1000 in FSA account, he has a similarly odds of out of pocket costs to be $1000, $1500, $2000, $2500, $3000, $3500, $4000 and $4500.  

Expected advantage = 1/8 (benefit when health cost is $1000) + 1/8 (advantage when health $1500) + 1/8(advantage when health $2000) + 1/8 (advantage when health $2500) + 1/8 (advantage when health $3000) + 1/8 (advantage when health $3500) + 1/8 (advantage when health $4000) + 1/8 (advantage when health $4500)  

Advantage for each situation is the sum individual spare from conclusion in charge by adding to FSA account.  

= 8( (1/8)×296.5)  

= 296.5  

In the event that he contributing $1500, at that point when the health consumption is simply $100, $500 returns to the utilize and the individual lost it so the advantage of contributing $1500 on the FSA account is originating from charge reasoning which is equivalent to $444.75 and he bear lost $500 as he unfit to utilize it, so the net advantage is - $55.25.  

Expected advantage = 1/8 (- $55.25) + 7 (81×296.5)  

= - $6.91 + 259.44  

= $252.53  

As the commitment builds the normal advantage diminishes, so the normal advantage is boosted where he contributes $1000.