math for liberal arts assignment

Oct 7th, 2015
Anonymous
Category:
Mathematics
Price: $5 USD

Question description

Pick a unique real problem and try to solve it using the consumer math solving strategies from this unit. Present the problem and the solution to the rest of the class.  View the problems posted by your classmates and respond to at least two. Read the Consumer Math Application Directions for detailed directions.

Pick a problem:

Find a problem in your life that you can solve using the consumer math that you learned in this unit.  Most of us have home, car, or education loans for which we sometimes need to calculate payments or time required to repay.  Many also have savings accounts or other investments and want to calculate growth in value over a period of time.

Solve the problem:

Use the consumer math learned in this unit to solve your problem.  The better you use the appropriate mathematics to correctly solve the problem, the more points you will earn.

Example:  

Last summer my husband and I purchased a new washer and dryer. The store was running a sale, so for the both of them they were asking for $1475. We paid $550 up front, and agreed to pay the rest of the balance a 4% add-on rate for the next 2 year.

Amount to be financed = $1475 – $650 = $825

Amount to repaid = P (1 + rt)

= $825 (1 + 0.04 x 2)

= $891

Monthly payment = $891/24 = 37.12

Total cost of purchase = $650 + 891 = 1541

According to these calculations we paid $66 more than the original cost.

OR

Statement of the problem

One bank nearby advertises a savings account with an annual interest rate of 1%, compounded monthly.  Another bank, all the way across town, advertises a savings account with an annual interest rate of 1%, compounded daily.

I have $5000 to invest, and I will not touch my savings for 5 years.  I remember from MTH 151 that compounding more frequently gives a higher total return on my investment. Is it worth the extra time and distance to go to the bank across town? For the purpose of this problem, let’s assume that neither bank offers online services, or that I prefer to deal with my banker in person.

Solution of the problem

The formula for compound interest is  

where amount after n compounding periods

 initial amount invested

 annual interest rate

 number of compounding periods per year.

For the nearby bank,  

For the across town bank,  

Although in 5 years, the interest would indeed be greater for the across town bank, the difference is only $1.30, so it is probably more worthwhile to use the nearby bank.

Other Topics:  mortgages, loans, credit cards


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