I need help with making a piece wise function for three jobs

Question

Job A: This job pays $1850 per month plus a bonus of $250 per month. However, you will not receive the bonus on a monthly basis. It will be placed into an account (Paying no interest). After you have worked for the company for 30 months you will receive, in a lump sum, all the money in the account at that time. If you quit before 30 months, you will receive none of the bonus money. Then, beginning with the 31st month, the $250 bonus will again be placed into the savings account each month for the remaining time you work for the company. At the end of the 60 months, you will receive, in a lump sum, the remaining bonus money. If you quit before the 60 months, you will receive none of the bonus money that accumulated beginning with the 31st month.

 

Job B: This job pays $2250 per month, but offers no bonus.

 

Job C: This job pays $1700 per month and offers a one-time bonus of $21250 at the end of the 35 months.

 

Remember that the decision has to be made after I have worked at job a for 25 months exactly.

Also, which job is better in the long run.

Answer 1

Make a chart

 

                     30 months              35 months               60 months

 

A            30(1850) + 30(250)    63,00+5(1850)       60(1850) + 60(250)

                      63,000                    72,250                     126,000

 

B                  30(2250)                  35(2250)                  60(2250)

                      67,500                     78,750                     135,000

 

C                                            35(1700) + 2150

                                                     80,750

 

In the short run (35 months) job C has the most income. For the long run (60 months) go with job B.

Answer 2

I must assume Job C is a one-time bonus of $21,250 after the first 35 months and that you would NOT get additional bonuses at 70 months, 105 months, etc.

 

In short term (25 months):

 

Job A: $1850 x 25 = $46,250.00 (you forfeit bonus money (less than 30 months) of 25 months of $250.00 per month)

 

Job B: $2250 x 25 = $56,250.00 (no bonus money)

 

Job C: $1700 x 25 = $42,500.00 (you forfeit one-time bonus money of $21,250.00 because it is less than 35 months)

 

 

In long term (let's say 60 months):
 
Job A: $1850 x 60 plus 2 sets of bonus money $250 x 30 x 2 =$126,000 (moving forward, every set of 30 months pays you $1850 + $250 = $2100 per month)
 
Job B: $2250 x 60 = $135,000.00 (moving forward, $2250 per month)

 

Job C: $1700 x 60 plus $21,250.00 one-time bonus after 35 months = $123,250.00 (moving forward, $1700 per month)

 

Conclusion:

 

Short term: 25 months - Choose Job B with expected value of $56,250.00

 

Long term: 60 months - Choose Job B with expected value of $135,000.00

 

Moving forward after 60 months: Choose Job B with monthly payment of $2,250.00