Question 1164435: On March 1st, 2012 of her freshman year at Science Park High School, Jessica started working 2 jobs after school. (She is working in her parents’ store and does not need working papers.) She works the same number of hours every week. Jessica decided to save all her money to purchase a new car after she graduates.
After five weeks of work, she had $1,570 saved. After ten weeks, she saved $2,453.
Write a function that represents Jessica’s savings.
x= weeks y=money earned
Coordinates: (5,1570)(10,2453) y=mx+b
m=y2-y1 / x2-x1 y=176.6x+b
m=2453-1570 / 10-5 2453=176.6(10)+b
m=88/5 2453=1766+b
m=176.6 - 1766 -1766
687=b
f(x)=176.6x+687.
At the beginning of the 53rd week, Jessica decided to stop working and invest all her savings in a corporate bond. The bond pays 9% interest compounded quarterly. Jessica decided to invest the money for a period of 2 years. Note that Jessica cannot withdraw money or sell the corporate bond before the end of the term.
Write a function that models her investment.
P= f(x)=176.6x+687.
P= 176.6(53)+687
P= 10,046.8
y=a(b)^x
y=10,046.8(1+0.09)^2
y=10,046.8(1.09)^2
y=10,046.8(1.1881)
y=11,936.60308 ~11,936.60
At the end of the 2-year investment, Jessica decided to purchase a new car for $18,000. It will be financed over a period of 48 months with 0% interest.
If she put $2,000 as down payment, how much does she need to pay each month?
Turns out that this was a lucky car for Jessica! The day she signed the purchase agreement and drove it out of the lot, she got her long-awaited surprise. Jessica got accepted to MIT! She was required to move in after 5 months from receiving the acceptance letter. As she moved to Cambridge, she decided to take a job that pays $3,200 a month. Her employer will deduct 12.6% in taxes from her paycheck. She also has a grant that pays all her university tuition. However, she needs to rent a studio for $1,500 per month, including utility. She estimated that her living expenses will cost $347 per week.
With her monthly car payments in mind, create a function of her savings during her 4 years at Cambridge, MA. How much money would she have at the end of her 4 years residency in Massachusetts?
Graph Jessica’s savings since she started working until her graduation from MIT in May 2020.
Answer by ikleyn(52775)   (Show Source):
You can put this solution on YOUR website! .
It is strange to me to see this post.
I used to think that a Math problem is a compact text not more than 5 lines of a standard width.
What I see here, is much more.
Is it a dissertation or some Master's degree thesis/foliant ?
Let me tell you honestly, that rare tutor (if any) will read it in whole, from the beginning to the end.
Me personally definitely will not.
But, nevertheless, to be in help, let me notice that the part (the formula and calculations) related to a two-year
investment compounded quarterly at 9% per year is INCORRECT.
To learn this subject, look into my lesson
- Compound interest percentage problems
- Problems on discretely compound accounts
in this site, and learn the subject from there.
Good luck.
My advise to you is to change your writing style, if you want to get help from this forum/site.
To change to what ? --- To a standard style writing Math problems . . .
Are you familiar with it ?
If not, explore any textbook on the School Math.
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And one more advise of great importance : No more than one problem per post, please.
It is the RULE, the POLICY and the REQUIREMENT of this forum.
Those who violate it, work against their own interests.
Have a nice day (!)
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