Assignment Details: Math 133, 1302A, College Algebra

Question

Assignment Detailmath133 1302a 01 College Algebraassignmentnameunit The Discussion Board (DB) is a core component of online learning that requires active participation from students and the instructor to foster interaction and dialogue. Each student must create an original response to an open-ended question and respond to at least two posts by peers throughout the week. The first post is due by Wednesday midnight (Central Time), with two additional responses afterward. Posts made after the unit ends will not be accepted. The purpose of the DB is for students to share ideas and relate course content through discussion. In this assignment, you will examine applications of linear functions related to car loans. Using the formula F(r) = (pt)r + p, where r is the interest rate and F(r) is the total cost of the car, you will calculate the total cost based on your chosen car's sale price (p), the loan term (t), and interest rates obtained from references. You will determine the interest on the loan, calculate total costs, model the total cost as a linear function, and find monthly payments. Then, you will analyze the savings when the interest rate is reduced by 1%, comparing the new total and monthly payments with the original.

Dr. Jack HW Helper · Accepted Answer

The discussion of simple interest car loans exemplifies the practical applications of linear functions in financial mathematics. By examining the relationship between interest rates and total loan costs, students can better grasp how variations in interest affect overall expenses and monthly payments. In this analysis, I will select a specific car's sale price, determine relevant interest rates, and compute total costs under different scenarios to elucidate these principles. Firstly, I identified my dream car's sale price, which is $25,000, based on current market listings (Kelley Blue Book, 2023). Next, I researched interest rates at local banks and online lenders; I found that the typical annual interest rate for a 60-month auto loan is approximately 4.5% (Bank of America, 2023). Applying the promotion, which reduces the rate by 1%, the interest rate becomes 3.5%. Converting this to a decimal, r = 0.035. For the purposes of this exercise, I selected a loan term of 5 years (t = 5). Using the formula for interest, I calculated: I = p × t × r = $25,000 × 5 × 0.035 = $4,375. The total cost of the loan, including the principal, is then: Total cost = p + interest = $25,000 + $4,375 = $29,375. Modeling the total cost as a linear function of the interest rate, the formula is TC(r) = (pt)r + p, leading to TC(r) = ($25,000)(5)r + $25,000 = $125,000r + $25,000. When dividing the total cost by the total number of months (60 months for 5 years), the monthly payment is $29,375 ÷ 60 ≈ $489.58. To analyze the impact of the interest rate reduction, I also calculated the total cost and monthly payment at the original interest rate of 4.5% before the reduction (r = 0.045). The interest on the loan was I = $25,000 × 5 × 0.045 = $5,625, resulting in a total cost of $30,625. The corresponding monthly payment is $30,625 ÷ 60 ≈ $510.42. The savings in total interest payment by taking advantage of the 1% rate reduction is $5,625 - $4,375 = $1,250. The monthly savings amount to $510.42 - $

Assignment Details: Math 133, 1302A, College Algebra

Assignment Detailmath133 1302a 01 College Algebraassignmentnameunit

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Assignment Detailmath133 1302a 01 College Algebraassignmentnameunit

Paper For Above instruction

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