Discussion Board Week 1
This Unit 1 DB assignment is really about linear functions, the topic for this week’s unit, not about cars or simple interest loans. The car purchase and simple interest loans are used here in this DB assignment to show just one of the common applications where a linear function may be useful in a real situation. Because this DB assignment is about linear functions, your main post should clearly show HOW this simple interest situation is an application of linear functions. The slope-intercept form of a linear function is usually stated as: y = mx + b, where x and y are the variables, m is the slope of the line, and b is the y-intercept. The linear function form in this assignment is: F(t) = (pr)t + p, where (pr) is playing the role of m, p is playing the role of b, t is playing the role of x, and F(t) is playing the role of y. In “function-speak”, the t is the independent (horizontal) variable and F(t) is the dependent (vertical) variable. Your post should clearly show this connection between what you are calculating and the slope-intercept form of a linear function.
Discussion Board Week 1
According to AOL autos (2012), a Jeep Grand Cherokee, Laredo 4dr 4?2, is sold at $27, 695 assuming sales tax not inclusive. For one to determine the annual interest rate for loan taken out to but the car, one has to calculate the interest on the original price that will have accrued depending on the interest rate. Capital One new car loans are offered at different rates for different periods.
These options include 2.99% for 36 months, 3.39% for 48 to 68 months and 3.99 % for 66 to 72 months (Capital one 2012).
To select a rate of 3.39% coincides with a period of 48 months to 68 months. To reduce the rate by 1%:
r = 3.39%-0.01%
= 2.39% = 0.0239
Time on the other hand is denoted t. in this case t = 48 months. 48 months in this instance translates to 4 years. Therefore, t = 4years.
To determine the interest rate, one has to employ the formula: interest = sale price * rate * time.
Interest = $27, 695 * 0.0339 * 4= $3755.442
To determine the total cost of the loan, the formula Total cost = (sale price*rate) time + Sale Price
Total price = ($27, 695*0.0339)4 + $27, 695
= $3755.442 + $27, 695
To determine the monthly installment, one has to divide the total cost by the number of months in the four years.
$31,450.422/48 = $655.217524 for every month.
If the rate were to be reduced by 1%, the cost is as follows.
Interest = $27, 695 * 0.0239 * 4= $2614.408
Total price = ($27, 695*0.0239)4 + $27, 695
= $2614.408 + $27, 695
Total amount saved = $31,450.422 – $30,309.408 = 1141.014
The calculations above are the principles involved in interest rates with regard to loans. An interest rate is referred to the fee at which interest is paid by a borrower to a lender, mostly banks (Coryn et al 1997). In the first step, the calculations determine the interest rate by multiplying the sale price, rate and time. The second step is aimed at calculating the total cost inclusive of the interest rate. When banks lend out money to a borrower, they expect to make a profit from the loan (Smith 2012). This usually comes inform of interest rate. In addition to returning the whole amount borrowed, one has to pay interest. To determine the monthly installment, divide the total cost by the total number of months within which one pays the loan (Hufner & Koske 2008). If the rate on interest is reduced by one percent over the same period, the subsequent interest paid is lower. This has been evidenced by the calculations that follow. The calculations show that a lower interest rate amounts to significant savings (Mankiw 2007). This is one of the reasons behind high levels of borrowing. People tend to borrow more from banks when interest rates are low (Taylor 2004).
Aol Autos (02 November 2012). 2013 Jeep Grand Cherokee. Retrieved from http://autos.aol.com/cars-Jeep-Grand+Cherokee-2013/pricing/
Capital One (02 November 2012). New Car Loans. Retrieved from http://www.capitalone.com/auto-financing/auto-loans/?Log=1&EventType=Link&ComponentType=T&LOB=MTS%3A%3ALCTML6KG4&PageName=Auto+Loans&PortletLocation=4%3B4-12-col%3B1-1-1&ComponentName=secondary_nav&ContentElement=4%3BNew+Car+Loans&TargetLob=MTS%3A%3ALCTML6KG4&TargetPageName=New+Car&referer=www.capitalone.com
Coryn G. A. & Mays E.(1997). Interest rate risk models: theory and practice.
Hu?fner, F., & Koske, I. (January 01, 2008). The Euro Changeover in the Slovak Republic: Implications for Inflation and Interest Rates.
Mankiw, N. G. (2004). Principles of macroeconomics. Mason, Ohio: Thomson/South-Western.
Smith, K. J. (2008). Mathematics: Its power and utility. Pacific Grove, Calif: Brooks/Cole.
Taylor, J. B. (2004). Principles of macroeconomics. Boston [u.a.: Houghton Mifflin.