{"id":3980,"date":"2023-06-05T16:21:21","date_gmt":"2023-06-05T16:21:21","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=3980"},"modified":"2026-03-23T17:47:17","modified_gmt":"2026-03-23T17:47:17","slug":"cars-fresh-take","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/cars-fresh-take\/","title":{"raw":"Cars: Fresh Take","rendered":"Cars: Fresh Take"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Calculate the monthly payment and interest expenses of a car loan<\/li>\r\n\t<li>Compare costs and pros and cons of leasing, owning a new car, and owning a used car<\/li>\r\n\t<li>Determine the costs associated with operating a car, such as gas mileage, fuel costs, and savings for maintenance expenses<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>The Basics of Car Purchasing<\/h2>\r\n<p>Before purchasing a car, you need to answer two critical questions: What do you want in a car, and what do you need? Do you need a new car, or would a used one serve your needs? Are there specific features you want, like assisted driving? Remember, any additional features beyond the standard ones will increase the cost.<\/p>\r\n<p>When considering your budget for a car, remember to factor in not just the car payment, but also the costs of insurance, maintenance, and upkeep. With a clear idea of what you can afford, you can then find a car that aligns with both your desires and your budget.<\/p>\r\n<p>The sticker price or the negotiated price of a car is not the final cost. There are various additional fees, and potentially sales tax, which add to the overall expense.<\/p>\r\n<section class=\"textbox example\">Luther negotiates for the price of his car, reaching agreement at [latex]$28,975[\/latex]. He needs to pay [latex]8\\%[\/latex] in sales tax, [latex]2.1\\%[\/latex] in ownership tax, a [latex]$950[\/latex] destination fee, processing fees totaling [latex]$370[\/latex], and registration fee of [latex]$617[\/latex]. What is the total cost for Luther\u2019s purchase?<br \/>\r\n[reveal-answer q=\"160930\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"160930\"]<br \/>\r\nThe sales tax is [latex]8\\%[\/latex] of the price of the car, and the ownership tax is [latex]2.1\\%[\/latex] of the price of the car.<br \/>\r\n<br \/>\r\nSales Tax = [latex]28,975 * .08 = $2,318[\/latex].<br \/>\r\n<br \/>\r\nOwnership Tax = [latex]28,975 * .021 = $608.475[\/latex].<br \/>\r\n<br \/>\r\nSo, the total tax is [latex]$2,318 + $608.475 = $2,926.475[\/latex].<br \/>\r\n<br \/>\r\nNext, we add the destination fee, processing fees, and registration fee:<br \/>\r\n<br \/>\r\n[latex]$950[\/latex] (destination fee) [latex]+ $370[\/latex] (processing fees) [latex]+ $617[\/latex] (registration fee) [latex]= $1,937[\/latex].<br \/>\r\n<br \/>\r\nNow, we add the cost of the car, the total tax, and the additional fees:<br \/>\r\n<br \/>\r\n[latex]$28,975[\/latex] (car price) [latex]+ $2,926.475[\/latex] (total tax) [latex]+ $1,937[\/latex] (additional fees) [latex]= $33,838.475[\/latex].<br \/>\r\n<br \/>\r\nSo, Luther's total cost for the purchase is approximately [latex]$33,838.48[\/latex], if we round to the nearest cent.[\/hidden-answer]<\/section>\r\n<h2>Car Loans<\/h2>\r\n<div class=\"textbox shaded\">\r\n<p><strong>The Main Idea\u00a0<\/strong><\/p>\r\n<p><strong>Car loans<\/strong> are a type of installment loan. Unlike a revolving line of credit, such as a credit card, an installment loan has a fixed loan amount, fixed interest rate, and fixed repayment schedule. Each payment made towards an installment loan consists of both principal (the original loan amount) and interest (the cost of borrowing). Installment loans provide borrowers with the benefit of predictable monthly payments, making it easier to budget and plan for loan repayment. By making regular payments, borrowers gradually reduce their loan balance until it is fully paid off, thereby fulfilling their financial obligations.<\/p>\r\n<\/div>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>loan payment formula<\/h3>\r\n<p>The payment, [latex]PMT[\/latex], per period to pay off a loan with with a beginning principal (loan amount) [latex]P[\/latex] is<\/p>\r\n<p>&nbsp;<\/p>\r\n<center>[latex]PMT = \\frac{P(\\frac{r}{n})}{1-(1+\\frac{r}{n})^{-nt}}[\/latex]<\/center>\r\n<p>&nbsp;<\/p>\r\n<p>where [latex]r[\/latex] is the annual interest rate in decimal form, [latex]t[\/latex] is the term in years of the loan, and [latex]n[\/latex] is the number of payments per year (typically, loans are paid monthly making [latex]n = 12[\/latex]).<\/p>\r\n<p>Note, payment to lenders is always rounded up to the next penny.<\/p>\r\n<\/div>\r\n<\/section>\r\n<section class=\"textbox questionHelp\">Often, the formula takes the form [latex]PMT = \\frac{Pr(1+r)^n}{(1+r)^n -1}[\/latex], where [latex]r[\/latex] is the interest rate per period (annual rate divided by the number of periods per year), and [latex]n[\/latex] is the total number of payments to be made.It is important to note the difference between [latex]r[\/latex] in this formula and the [latex]r[\/latex] in the formula given previously.<\/section>\r\n<p>The difference between financing a new car or a used car is that financing a new car typically comes with a lower interest rate and a longer term that financing a used car.<\/p>\r\n<section class=\"textbox watchIt\"><iframe src=\"\/\/plugin.3playmedia.com\/show?mf=10356041&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=p8f8XP2tmvE&amp;video_target=tpm-plugin-v79yzmaa-p8f8XP2tmvE\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/How+To+Calculate+Your+Car+Loan+Paymen.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cHow To Calculate Your Car Loan Payment\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<section class=\"textbox example\">In the following, calculate the monthly payment using the given total to be financed, the interest rate, and the term of the car loan.\r\n\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>Total to be financed is [latex]$18,325[\/latex], interest rate is [latex]6.75\\%[\/latex], for [latex]4[\/latex] years.<\/li>\r\n\t<li>Total to be financed is [latex]$41,633[\/latex], interest rate is [latex]3.9\\%[\/latex], for [latex]6[\/latex] years.<\/li>\r\n<\/ol>\r\n<p>[reveal-answer q=\"160931\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"160931\"]<\/p>\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>The amount to be financed is the principal, [latex]P[\/latex], which is [latex]$18,325[\/latex]. The rate [latex]r[\/latex] is [latex]0.0675[\/latex], and the term is [latex]t = 4[\/latex] years. These are monthly payments, so [latex]n = 12[\/latex]. Substituting and calculating, we find the monthly payment to be<center>[latex]$436.70[\/latex]<\/center>\u00a0<\/li>\r\n\t<li>The amount to be financed is the principal, [latex]P[\/latex], which is [latex]$41,633[\/latex]. The rate [latex]r[\/latex] is [latex]0.039[\/latex], and the term is [latex]t = 6[\/latex] years. These are monthly payments, so [latex]n = 12[\/latex]. Substituting and calculating, we find the monthly payment to be<center>[latex]$649.47[\/latex]<\/center><\/li>\r\n<\/ol>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<p>One way to bring down payments on a car is to provide a down payment. A down payment is a large initial payment made during the purchase of a car. This upfront payment significantly reduces the amount of money you have to borrow, which in turn lowers your monthly payments and total financing costs. Making a down payment can have several benefits:<\/p>\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li style=\"list-style-type: none;\">\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>Lower Monthly Payments: By reducing the amount you need to borrow, a down payment reduces your monthly loan payments.<\/li>\r\n\t<li>Reduced Interest Costs: A smaller loan means less interest paid over the life of the loan.<\/li>\r\n\t<li>Improved Loan Approval Chances: A down payment can make you a less risky borrower, improving your chances of loan approval.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<section class=\"textbox example\">Carlos buys a car with a negotiated price of [latex]$36,250[\/latex]. The sales tax in his region is [latex]6.5\\%[\/latex]. The dealer charges a [latex]$1,200[\/latex] destination fee and a [latex]$450[\/latex] documentation fee. He must pay for title, registration, and license plates, which come to [latex]$21.50[\/latex]. If he has a [latex]$7,500[\/latex] down payment, how much will he have to finance?<br \/>\r\n[reveal-answer q=\"160932\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"160932\"]<br \/>\r\n<center>[latex]$32,777.75[\/latex]<\/center><br \/>\r\n[\/hidden-answer]<\/section>\r\n<h2>The Basics of Leasing a Car<\/h2>\r\n<div class=\"textbox shaded\">\r\n<p><strong>The Main Idea\u00a0<\/strong><\/p>\r\n<p>Leasing a car is comparable to renting a vehicle for a set duration, generally a few years, where you make monthly payments to a leasing company or dealership without owning the car. It provides the advantage of enjoying a new car without a long-term commitment or financial ownership burden, but often includes mileage restrictions that may incur additional fees if exceeded.<\/p>\r\n<p>Lease payments, akin to regular loan payments, are calculated using specific variables: the negotiated price of the car, its residual value (the car's estimated worth at the end of the lease), the length of the lease, the monthly depreciation (the monthly value loss of the car), and the Money Factor (MF), which is a unique interest rate for leases. These elements together form the structure of a car lease payment.<\/p>\r\n<\/div>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>monthly depreciation and money factor formulas<\/h3>\r\n<p>The monthly depreciation for a car, [latex]MD[\/latex], is [latex]MD=\\frac{P\u2212R}{n}[\/latex]. Where [latex]P[\/latex] is the price paid for the car, [latex]R[\/latex] is the residual value of the car, and [latex]n[\/latex] is the number of months of the lease.<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>The annual percentage rate for a lease is [latex]APR=2400\u00d7MF[\/latex], where [latex]MF[\/latex] is the money factor of the lease. The [latex]MF[\/latex] for a lease is [latex]MF=\\frac{APR}{2,400}[\/latex].<\/p>\r\n<\/div>\r\n<\/section>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>lease payment formula<\/h3>\r\n<p>The payment, [latex]PMT[\/latex], for a lease is [latex]PMT=\\frac{(P\u2212R)}{n}+(P+R)\u00d7MF[\/latex], where [latex]P[\/latex] is the price paid for the car, [latex]R[\/latex] is the residual value of the car, [latex]n[\/latex] is the number of months of the lease, and [latex]MF[\/latex] is the money factor for the lease.<\/p>\r\n<\/div>\r\n<\/section>\r\n<section class=\"textbox example\">RJ wants to lease a Tahoe in Salt Lake City, Utah. Find the total cost of obtaining his lease if he has a [latex]$5,000.00[\/latex] down payment, [latex]$225[\/latex] in acquisition fees, a security deposit of [latex]$750.00[\/latex], [latex]$500.00[\/latex] in disposition fees, and sales tax of [latex]$4,092[\/latex].<br \/>\r\n[reveal-answer q=\"160933\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"160933\"]<br \/>\r\nAdding these values together and we find the total cost is [latex]$10,567.00[\/latex].<br \/>\r\n[\/hidden-answer]<\/section>\r\n<section class=\"textbox example\">The purchase price of a car is [latex]$27,500[\/latex]. Its residual price is [latex]$17,875[\/latex]. What is its monthly depreciation for a [latex]24[\/latex]-month lease?[reveal-answer q=\"160934\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"160934\"]<br \/>\r\nThe monthly depreciation formula is [latex]MD=\\frac{P\u2212R}{n}[\/latex], Substituting [latex]$27,500[\/latex] for [latex]P[\/latex], [latex]$17,875[\/latex] for [latex]R[\/latex], and [latex]24[\/latex] for [latex]n[\/latex], we find [latex]MD[\/latex] to be<center>[latex]MD=\\frac{P\u2212R}{n}=\\frac{$27,500\u2212$17,875}{24}=\\frac{$9,625}{24}=$401.04[\/latex]<\/center><br \/>\r\n[\/hidden-answer]<\/section>\r\n<section class=\"textbox example\">\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>Find the annual percentage rate if the money factor is [latex]0.00001208\\overline{3}[\/latex].<\/li>\r\n\t<li>Find the money factor if the APR is [latex]7.9\\%[\/latex].<\/li>\r\n<\/ol>\r\n<p>[reveal-answer q=\"160935\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"160935\"]<\/p>\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>The APR is the money factor times [latex]2400[\/latex], so [latex]APR=2400\u00d7MF=2400\u00d70.00001208\\overline{3}=0.0289[\/latex]. Expressed as a percentage, the APR is [latex]2.89\\%[\/latex].<\/li>\r\n\t<li>The MF is the APR divided by [latex]2400[\/latex], so [latex]MF=\\frac{APR}{2400}=\\frac{0.079}{2400}=\u200b\u200b\u200b0.00003291\\overline{6}[\/latex].<\/li>\r\n<\/ol>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox example\">Calculate the lease payments for car with the following price, residual price, length of lease, and money factor or APR.\r\n\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>Price is [latex]$38,750[\/latex], residual price is [latex]$18,140.16[\/latex], [latex]36[\/latex]-month lease, money factor is [latex]0.000035[\/latex].<\/li>\r\n\t<li>Price is [latex]$45,600[\/latex], residual price is [latex]$21,312.50[\/latex], [latex]24[\/latex]-month lease, APR is [latex]11.7\\%[\/latex].<\/li>\r\n<\/ol>\r\n<p>[reveal-answer q=\"160936\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"160936\"]<\/p>\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>Substituting the values [latex]P = $38,750[\/latex], [latex]R = $18,140.16[\/latex], [latex]n = 36[\/latex] and [latex]MF = 0.000035[\/latex] into the formula and calculating, the monthly lease payment is<center>[latex]\\begin{array}{ll}<br \/>\r\nPMT &amp;&amp;=\\frac{(P\u2212R)}{n}+(P+R)\u00d7MF \\\\<br \/>\r\n&amp;&amp; =\\frac{($38,750\u2212$18,140.16)}{36}+($38,750+$18,140.16)\u00d70.000035 \\\\<br \/>\r\n&amp;&amp; =\\frac{($20,609.84)}{36}+($56,890.16)\u00d70.000035 \\\\<br \/>\r\n&amp;&amp; = \\$574.49 \\\\<br \/>\r\n\\end{array}[\/latex]<br \/>\r\n<br \/>\r\n<\/center><\/li>\r\n\t<li>Given the APR, we find the MF which is [latex]MF=\\frac{APR}{2400}=\\frac{0.117}{2400}=0.00004875[\/latex]. Substituting the values [latex]P = $45,600[\/latex], [latex]R = $21,312.50[\/latex], [latex]n = 24[\/latex] and the MF into the formula and calculating, the monthly lease payment is<center>[latex]\\begin{array}{ll}<br \/>\r\nPMT &amp;&amp;=\\frac{(P\u2212R)}{n}+(P+R)\u00d7MF \\\\<br \/>\r\n&amp;&amp; =\\frac{($45,600\u2212$21,312.50)}{24}+($45,600+$21,312.50)\u00d70.00004875 \\\\<br \/>\r\n&amp;&amp; =\\frac{($24,287.50)}{24}+($66,912.50)\u00d70.00004875 \\\\<br \/>\r\n&amp;&amp; = \\$1,015.24 \\\\<br \/>\r\n\\end{array}[\/latex]<\/center><\/li>\r\n<\/ol>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox watchIt\"><iframe src=\"\/\/plugin.3playmedia.com\/show?mf=10356042&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=gI8KB-QJawI&amp;video_target=tpm-plugin-as9lcbjh-gI8KB-QJawI\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Car+Lease+Explained+In+United+States+(Animated).txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cCar Lease Explained In United States (Animated)\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<h2>Understanding the True Cost of Owning a Car<\/h2>\r\n<h3>Car Insurance<\/h3>\r\n<div class=\"textbox shaded\">\r\n<p><strong>The Main Idea\u00a0<\/strong><\/p>\r\n<p>Car insurance, a necessary cost regardless of whether you lease or own a car, provides coverage for various potential expenses related to accidents and car damage. Most states mandate at least some level of insurance, with liability insurance often being compulsory. Other insurance types include collision insurance, comprehensive insurance, uninsured or underinsured motorist insurance, medical payments insurance, personal injury protection insurance, gap insurance, and rental reimbursement insurance, among others. Each type covers different aspects of car-related expenses and the cost of insurance can vary greatly depending on personal factors such as age, driving record, and place of residence. The cost of insurance should be factored into the affordability of a car.<\/p>\r\n<\/div>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/HOPQAwp1Nrk\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/The+Major+Types+Of+Car+Insurance+Explained.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cThe Major Types Of Car Insurance Explained\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<section class=\"textbox example\">\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>Which component of insurance covers medical bills in the event of an accident?<\/li>\r\n\t<li>Which component of insurance pays for costs to others if you have an accident and are found legally responsible for those damages?<\/li>\r\n<\/ol>\r\n<p>[reveal-answer q=\"160937\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"160937\"]<\/p>\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>Personal injury protection<\/li>\r\n\t<li>Liability insurance<\/li>\r\n<\/ol>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox example\">If your car payment is [latex]$410.86[\/latex] per month and your car insurance is [latex]$2,190[\/latex] per year, what is the cost of the car per month when accounting for the insurance?<br \/>\r\n[reveal-answer q=\"160938\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"160938\"]<br \/>\r\nThe cost of the car including insurance is the monthly payment, [latex]$410.86[\/latex], plus the monthly cost of the insurance. The insurance cost per month is [latex]\\frac{$2,190}{12}=$182.50[\/latex] since the insurance cost is for [latex]12[\/latex] months. Adding those the cost with insurance is [latex]$593.36[\/latex].<br \/>\r\n[\/hidden-answer]<\/section>\r\n<h3>Maintaining a Car<\/h3>\r\n<div class=\"textbox shaded\">\r\n<p><strong>The Main Idea\u00a0<\/strong><\/p>\r\n<p>Owning a car involves not just the initial purchase but also ongoing maintenance costs. These can include expenses for fuel, tire replacements, oil changes, windshield wiper replacements, annual inspections, brake pad replacements, and air filter changes. The cost range and frequency of these requirements vary, but all should be included in the budget for owning a car. Additionally, a financial buffer should be kept for unexpected, potentially costly, repairs.<\/p>\r\n<\/div>\r\n<section class=\"textbox linkToLearning\" aria-label=\"Link to Learning\">\r\n<p><a href=\"https:\/\/www.khanacademy.org\/economics-finance-domain\/economics-personal-finance-va\/x3ed8f3aede624754:car-buying\/x3ed8f3aede624754:cost-of-car-ownership\/v\/what-are-the-true-costs-of-car-ownership\" target=\"_blank\" rel=\"noopener\">Watch the video What Are the True Costs of Car Ownership?<\/a> or <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/What+Are+the+True+Costs+of+Car+Ownership_.txt\" target=\"_blank\" rel=\"noopener\">read the transcript of the video here<\/a>.<\/p>\r\n<\/section>\r\n<section class=\"textbox example\">Hana needs to budget for her car maintenance. She expects to buy new tires each [latex]5[\/latex] years, which will cost her [latex]$390[\/latex] to replace them all. Oil changes near her cost [latex]$59.99[\/latex], and she believes she will get one every [latex]3[\/latex] months. Her inspection costs [latex]$25[\/latex] per year. Wipers for her car cost [latex]$115[\/latex] for all three and she anticipates changing them every year. She drives less than [latex]30,000[\/latex] miles per year, so she plans to replace the air filter once per year. The air filter for her car costs [latex]$46.25[\/latex]. How much should she budget per month to cover these costs?[reveal-answer q=\"160939\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"160939\"]<br \/>\r\n[latex]$42.02[\/latex]<br \/>\r\n[\/hidden-answer]<\/section>\r\n<h3>Fuel Costs<\/h3>\r\n<div class=\"textbox shaded\">\r\n<p><strong>The Main Idea\u00a0<\/strong><\/p>\r\n<p>Fuel efficiency, or gas mileage, is an indicator of how far a vehicle can travel per unit of fuel, generally measured in miles per gallon (MPG). More efficient vehicles consume less fuel to cover a specific distance, thereby reducing fuel costs. Factors influencing fuel efficiency include vehicle size, weight, engine type, driving conditions, and habits. When buying a car, the EPA provides an estimated MPG for city, highway, and combined averages to aid comparisons. Knowing your car's typical MPG allows for annual fuel cost calculation.<\/p>\r\n<\/div>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>annual fuel cost<\/h3>\r\n<center>[latex]\\text{ annual fuel cost } = \\frac{\\text{miles driven annually}}{\\text{miles per gallon}} \\times \\text{ price per gallon of gas}[\/latex]<\/center><\/div>\r\n<\/section>\r\n<section class=\"textbox example\">You're deciding between two vehicles. Car J gets [latex]30[\/latex] MPG, and Car K gets [latex]40[\/latex] MPG. If you anticipate driving [latex]12,000[\/latex] miles per year and the price of gas is projected to be [latex]$4.00[\/latex] per gallon, how much would you save in gas costs annually by choosing Car K over Car J?<br \/>\r\n[reveal-answer q=\"160940\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"160940\"]<br \/>\r\nFirst, we need to determine the annual gas usage for each car:\r\n\r\n<ul>\r\n\t<li>For Car J, which gets [latex]30[\/latex] MPG: [latex]12,000[\/latex] miles [latex]\u00f7 30[\/latex] MPG [latex]= 400[\/latex] gallons per year<\/li>\r\n\t<li>For Car K, which gets [latex]40[\/latex] MPG: [latex]12,000[\/latex] miles [latex]\u00f7 40[\/latex] MPG [latex]= 300[\/latex] gallons per year<\/li>\r\n<\/ul>\r\n<p>Then, we can calculate the annual cost of gas for each car:<\/p>\r\n<ul>\r\n\t<li>For Car J: [latex]400[\/latex] gallons [latex]\\times $4.00[\/latex] per gallon [latex]= $1,600[\/latex]<\/li>\r\n\t<li>For Car K: [latex]300[\/latex] gallons [latex]\\times $4.00[\/latex] per gallon [latex]= $1,200[\/latex]<\/li>\r\n<\/ul>\r\n<p>Therefore, by choosing Car K, which is more fuel-efficient, you would save [latex]$400[\/latex] on gas costs per year given the stated conditions.<br \/>\r\n[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox watchIt\"><iframe src=\"\/\/plugin.3playmedia.com\/show?mf=10356040&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=4nrjpa34C1c&amp;video_target=tpm-plugin-dcqhvn0a-4nrjpa34C1c\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Everything+you+need+to+know+about+buying+a+car.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cEverything you need to know about buying a car\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Calculate the monthly payment and interest expenses of a car loan<\/li>\n<li>Compare costs and pros and cons of leasing, owning a new car, and owning a used car<\/li>\n<li>Determine the costs associated with operating a car, such as gas mileage, fuel costs, and savings for maintenance expenses<\/li>\n<\/ul>\n<\/section>\n<h2>The Basics of Car Purchasing<\/h2>\n<p>Before purchasing a car, you need to answer two critical questions: What do you want in a car, and what do you need? Do you need a new car, or would a used one serve your needs? Are there specific features you want, like assisted driving? Remember, any additional features beyond the standard ones will increase the cost.<\/p>\n<p>When considering your budget for a car, remember to factor in not just the car payment, but also the costs of insurance, maintenance, and upkeep. With a clear idea of what you can afford, you can then find a car that aligns with both your desires and your budget.<\/p>\n<p>The sticker price or the negotiated price of a car is not the final cost. There are various additional fees, and potentially sales tax, which add to the overall expense.<\/p>\n<section class=\"textbox example\">Luther negotiates for the price of his car, reaching agreement at [latex]$28,975[\/latex]. He needs to pay [latex]8\\%[\/latex] in sales tax, [latex]2.1\\%[\/latex] in ownership tax, a [latex]$950[\/latex] destination fee, processing fees totaling [latex]$370[\/latex], and registration fee of [latex]$617[\/latex]. What is the total cost for Luther\u2019s purchase?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160930\">Show Solution<\/button><\/p>\n<div id=\"q160930\" class=\"hidden-answer\" style=\"display: none\">\nThe sales tax is [latex]8\\%[\/latex] of the price of the car, and the ownership tax is [latex]2.1\\%[\/latex] of the price of the car.<\/p>\n<p>Sales Tax = [latex]28,975 * .08 = $2,318[\/latex].<\/p>\n<p>Ownership Tax = [latex]28,975 * .021 = $608.475[\/latex].<\/p>\n<p>So, the total tax is [latex]$2,318 + $608.475 = $2,926.475[\/latex].<\/p>\n<p>Next, we add the destination fee, processing fees, and registration fee:<\/p>\n<p>[latex]$950[\/latex] (destination fee) [latex]+ $370[\/latex] (processing fees) [latex]+ $617[\/latex] (registration fee) [latex]= $1,937[\/latex].<\/p>\n<p>Now, we add the cost of the car, the total tax, and the additional fees:<\/p>\n<p>[latex]$28,975[\/latex] (car price) [latex]+ $2,926.475[\/latex] (total tax) [latex]+ $1,937[\/latex] (additional fees) [latex]= $33,838.475[\/latex].<\/p>\n<p>So, Luther&#8217;s total cost for the purchase is approximately [latex]$33,838.48[\/latex], if we round to the nearest cent.<\/p><\/div>\n<\/div>\n<\/section>\n<h2>Car Loans<\/h2>\n<div class=\"textbox shaded\">\n<p><strong>The Main Idea\u00a0<\/strong><\/p>\n<p><strong>Car loans<\/strong> are a type of installment loan. Unlike a revolving line of credit, such as a credit card, an installment loan has a fixed loan amount, fixed interest rate, and fixed repayment schedule. Each payment made towards an installment loan consists of both principal (the original loan amount) and interest (the cost of borrowing). Installment loans provide borrowers with the benefit of predictable monthly payments, making it easier to budget and plan for loan repayment. By making regular payments, borrowers gradually reduce their loan balance until it is fully paid off, thereby fulfilling their financial obligations.<\/p>\n<\/div>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>loan payment formula<\/h3>\n<p>The payment, [latex]PMT[\/latex], per period to pay off a loan with with a beginning principal (loan amount) [latex]P[\/latex] is<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;\">[latex]PMT = \\frac{P(\\frac{r}{n})}{1-(1+\\frac{r}{n})^{-nt}}[\/latex]<\/div>\n<p>&nbsp;<\/p>\n<p>where [latex]r[\/latex] is the annual interest rate in decimal form, [latex]t[\/latex] is the term in years of the loan, and [latex]n[\/latex] is the number of payments per year (typically, loans are paid monthly making [latex]n = 12[\/latex]).<\/p>\n<p>Note, payment to lenders is always rounded up to the next penny.<\/p>\n<\/div>\n<\/section>\n<section class=\"textbox questionHelp\">Often, the formula takes the form [latex]PMT = \\frac{Pr(1+r)^n}{(1+r)^n -1}[\/latex], where [latex]r[\/latex] is the interest rate per period (annual rate divided by the number of periods per year), and [latex]n[\/latex] is the total number of payments to be made.It is important to note the difference between [latex]r[\/latex] in this formula and the [latex]r[\/latex] in the formula given previously.<\/section>\n<p>The difference between financing a new car or a used car is that financing a new car typically comes with a lower interest rate and a longer term that financing a used car.<\/p>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" src=\"\/\/plugin.3playmedia.com\/show?mf=10356041&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=p8f8XP2tmvE&amp;video_target=tpm-plugin-v79yzmaa-p8f8XP2tmvE\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/How+To+Calculate+Your+Car+Loan+Paymen.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cHow To Calculate Your Car Loan Payment\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<section class=\"textbox example\">In the following, calculate the monthly payment using the given total to be financed, the interest rate, and the term of the car loan.<\/p>\n<ol style=\"list-style-type: decimal;\">\n<li>Total to be financed is [latex]$18,325[\/latex], interest rate is [latex]6.75\\%[\/latex], for [latex]4[\/latex] years.<\/li>\n<li>Total to be financed is [latex]$41,633[\/latex], interest rate is [latex]3.9\\%[\/latex], for [latex]6[\/latex] years.<\/li>\n<\/ol>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160931\">Show Solution<\/button><\/p>\n<div id=\"q160931\" class=\"hidden-answer\" style=\"display: none\">\n<ol style=\"list-style-type: decimal;\">\n<li>The amount to be financed is the principal, [latex]P[\/latex], which is [latex]$18,325[\/latex]. The rate [latex]r[\/latex] is [latex]0.0675[\/latex], and the term is [latex]t = 4[\/latex] years. These are monthly payments, so [latex]n = 12[\/latex]. Substituting and calculating, we find the monthly payment to be\n<div style=\"text-align: center;\">[latex]$436.70[\/latex]<\/div>\n<p>\u00a0<\/li>\n<li>The amount to be financed is the principal, [latex]P[\/latex], which is [latex]$41,633[\/latex]. The rate [latex]r[\/latex] is [latex]0.039[\/latex], and the term is [latex]t = 6[\/latex] years. These are monthly payments, so [latex]n = 12[\/latex]. Substituting and calculating, we find the monthly payment to be\n<div style=\"text-align: center;\">[latex]$649.47[\/latex]<\/div>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n<p>One way to bring down payments on a car is to provide a down payment. A down payment is a large initial payment made during the purchase of a car. This upfront payment significantly reduces the amount of money you have to borrow, which in turn lowers your monthly payments and total financing costs. Making a down payment can have several benefits:<\/p>\n<ol style=\"list-style-type: decimal;\">\n<li style=\"list-style-type: none;\">\n<ol style=\"list-style-type: decimal;\">\n<li>Lower Monthly Payments: By reducing the amount you need to borrow, a down payment reduces your monthly loan payments.<\/li>\n<li>Reduced Interest Costs: A smaller loan means less interest paid over the life of the loan.<\/li>\n<li>Improved Loan Approval Chances: A down payment can make you a less risky borrower, improving your chances of loan approval.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<section class=\"textbox example\">Carlos buys a car with a negotiated price of [latex]$36,250[\/latex]. The sales tax in his region is [latex]6.5\\%[\/latex]. The dealer charges a [latex]$1,200[\/latex] destination fee and a [latex]$450[\/latex] documentation fee. He must pay for title, registration, and license plates, which come to [latex]$21.50[\/latex]. If he has a [latex]$7,500[\/latex] down payment, how much will he have to finance?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160932\">Show Solution<\/button><\/p>\n<div id=\"q160932\" class=\"hidden-answer\" style=\"display: none\"><\/p>\n<div style=\"text-align: center;\">[latex]$32,777.75[\/latex]<\/div>\n<p>\n<\/div>\n<\/div>\n<\/section>\n<h2>The Basics of Leasing a Car<\/h2>\n<div class=\"textbox shaded\">\n<p><strong>The Main Idea\u00a0<\/strong><\/p>\n<p>Leasing a car is comparable to renting a vehicle for a set duration, generally a few years, where you make monthly payments to a leasing company or dealership without owning the car. It provides the advantage of enjoying a new car without a long-term commitment or financial ownership burden, but often includes mileage restrictions that may incur additional fees if exceeded.<\/p>\n<p>Lease payments, akin to regular loan payments, are calculated using specific variables: the negotiated price of the car, its residual value (the car&#8217;s estimated worth at the end of the lease), the length of the lease, the monthly depreciation (the monthly value loss of the car), and the Money Factor (MF), which is a unique interest rate for leases. These elements together form the structure of a car lease payment.<\/p>\n<\/div>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>monthly depreciation and money factor formulas<\/h3>\n<p>The monthly depreciation for a car, [latex]MD[\/latex], is [latex]MD=\\frac{P\u2212R}{n}[\/latex]. Where [latex]P[\/latex] is the price paid for the car, [latex]R[\/latex] is the residual value of the car, and [latex]n[\/latex] is the number of months of the lease.<\/p>\n<p>&nbsp;<\/p>\n<p>The annual percentage rate for a lease is [latex]APR=2400\u00d7MF[\/latex], where [latex]MF[\/latex] is the money factor of the lease. The [latex]MF[\/latex] for a lease is [latex]MF=\\frac{APR}{2,400}[\/latex].<\/p>\n<\/div>\n<\/section>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>lease payment formula<\/h3>\n<p>The payment, [latex]PMT[\/latex], for a lease is [latex]PMT=\\frac{(P\u2212R)}{n}+(P+R)\u00d7MF[\/latex], where [latex]P[\/latex] is the price paid for the car, [latex]R[\/latex] is the residual value of the car, [latex]n[\/latex] is the number of months of the lease, and [latex]MF[\/latex] is the money factor for the lease.<\/p>\n<\/div>\n<\/section>\n<section class=\"textbox example\">RJ wants to lease a Tahoe in Salt Lake City, Utah. Find the total cost of obtaining his lease if he has a [latex]$5,000.00[\/latex] down payment, [latex]$225[\/latex] in acquisition fees, a security deposit of [latex]$750.00[\/latex], [latex]$500.00[\/latex] in disposition fees, and sales tax of [latex]$4,092[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160933\">Show Solution<\/button><\/p>\n<div id=\"q160933\" class=\"hidden-answer\" style=\"display: none\">\nAdding these values together and we find the total cost is [latex]$10,567.00[\/latex].\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\">The purchase price of a car is [latex]$27,500[\/latex]. Its residual price is [latex]$17,875[\/latex]. What is its monthly depreciation for a [latex]24[\/latex]-month lease?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160934\">Show Solution<\/button><\/p>\n<div id=\"q160934\" class=\"hidden-answer\" style=\"display: none\">\nThe monthly depreciation formula is [latex]MD=\\frac{P\u2212R}{n}[\/latex], Substituting [latex]$27,500[\/latex] for [latex]P[\/latex], [latex]$17,875[\/latex] for [latex]R[\/latex], and [latex]24[\/latex] for [latex]n[\/latex], we find [latex]MD[\/latex] to be<\/p>\n<div style=\"text-align: center;\">[latex]MD=\\frac{P\u2212R}{n}=\\frac{$27,500\u2212$17,875}{24}=\\frac{$9,625}{24}=$401.04[\/latex]<\/div>\n<p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\">\n<ol style=\"list-style-type: decimal;\">\n<li>Find the annual percentage rate if the money factor is [latex]0.00001208\\overline{3}[\/latex].<\/li>\n<li>Find the money factor if the APR is [latex]7.9\\%[\/latex].<\/li>\n<\/ol>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160935\">Show Solution<\/button><\/p>\n<div id=\"q160935\" class=\"hidden-answer\" style=\"display: none\">\n<ol style=\"list-style-type: decimal;\">\n<li>The APR is the money factor times [latex]2400[\/latex], so [latex]APR=2400\u00d7MF=2400\u00d70.00001208\\overline{3}=0.0289[\/latex]. Expressed as a percentage, the APR is [latex]2.89\\%[\/latex].<\/li>\n<li>The MF is the APR divided by [latex]2400[\/latex], so [latex]MF=\\frac{APR}{2400}=\\frac{0.079}{2400}=\u200b\u200b\u200b0.00003291\\overline{6}[\/latex].<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\">Calculate the lease payments for car with the following price, residual price, length of lease, and money factor or APR.<\/p>\n<ol style=\"list-style-type: decimal;\">\n<li>Price is [latex]$38,750[\/latex], residual price is [latex]$18,140.16[\/latex], [latex]36[\/latex]-month lease, money factor is [latex]0.000035[\/latex].<\/li>\n<li>Price is [latex]$45,600[\/latex], residual price is [latex]$21,312.50[\/latex], [latex]24[\/latex]-month lease, APR is [latex]11.7\\%[\/latex].<\/li>\n<\/ol>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160936\">Show Solution<\/button><\/p>\n<div id=\"q160936\" class=\"hidden-answer\" style=\"display: none\">\n<ol style=\"list-style-type: decimal;\">\n<li>Substituting the values [latex]P = $38,750[\/latex], [latex]R = $18,140.16[\/latex], [latex]n = 36[\/latex] and [latex]MF = 0.000035[\/latex] into the formula and calculating, the monthly lease payment is\n<div style=\"text-align: center;\">[latex]\\begin{array}{ll}<br \/>  PMT &&=\\frac{(P\u2212R)}{n}+(P+R)\u00d7MF \\\\<br \/>  && =\\frac{($38,750\u2212$18,140.16)}{36}+($38,750+$18,140.16)\u00d70.000035 \\\\<br \/>  && =\\frac{($20,609.84)}{36}+($56,890.16)\u00d70.000035 \\\\<br \/>  && = \\$574.49 \\\\<br \/>  \\end{array}[\/latex]<\/p>\n<\/div>\n<\/li>\n<li>Given the APR, we find the MF which is [latex]MF=\\frac{APR}{2400}=\\frac{0.117}{2400}=0.00004875[\/latex]. Substituting the values [latex]P = $45,600[\/latex], [latex]R = $21,312.50[\/latex], [latex]n = 24[\/latex] and the MF into the formula and calculating, the monthly lease payment is\n<div style=\"text-align: center;\">[latex]\\begin{array}{ll}<br \/>  PMT &&=\\frac{(P\u2212R)}{n}+(P+R)\u00d7MF \\\\<br \/>  && =\\frac{($45,600\u2212$21,312.50)}{24}+($45,600+$21,312.50)\u00d70.00004875 \\\\<br \/>  && =\\frac{($24,287.50)}{24}+($66,912.50)\u00d70.00004875 \\\\<br \/>  && = \\$1,015.24 \\\\<br \/>  \\end{array}[\/latex]<\/div>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" src=\"\/\/plugin.3playmedia.com\/show?mf=10356042&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=gI8KB-QJawI&amp;video_target=tpm-plugin-as9lcbjh-gI8KB-QJawI\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Car+Lease+Explained+In+United+States+(Animated).txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cCar Lease Explained In United States (Animated)\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<h2>Understanding the True Cost of Owning a Car<\/h2>\n<h3>Car Insurance<\/h3>\n<div class=\"textbox shaded\">\n<p><strong>The Main Idea\u00a0<\/strong><\/p>\n<p>Car insurance, a necessary cost regardless of whether you lease or own a car, provides coverage for various potential expenses related to accidents and car damage. Most states mandate at least some level of insurance, with liability insurance often being compulsory. Other insurance types include collision insurance, comprehensive insurance, uninsured or underinsured motorist insurance, medical payments insurance, personal injury protection insurance, gap insurance, and rental reimbursement insurance, among others. Each type covers different aspects of car-related expenses and the cost of insurance can vary greatly depending on personal factors such as age, driving record, and place of residence. The cost of insurance should be factored into the affordability of a car.<\/p>\n<\/div>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/HOPQAwp1Nrk\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/The+Major+Types+Of+Car+Insurance+Explained.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cThe Major Types Of Car Insurance Explained\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<section class=\"textbox example\">\n<ol style=\"list-style-type: decimal;\">\n<li>Which component of insurance covers medical bills in the event of an accident?<\/li>\n<li>Which component of insurance pays for costs to others if you have an accident and are found legally responsible for those damages?<\/li>\n<\/ol>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160937\">Show Solution<\/button><\/p>\n<div id=\"q160937\" class=\"hidden-answer\" style=\"display: none\">\n<ol style=\"list-style-type: decimal;\">\n<li>Personal injury protection<\/li>\n<li>Liability insurance<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\">If your car payment is [latex]$410.86[\/latex] per month and your car insurance is [latex]$2,190[\/latex] per year, what is the cost of the car per month when accounting for the insurance?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160938\">Show Solution<\/button><\/p>\n<div id=\"q160938\" class=\"hidden-answer\" style=\"display: none\">\nThe cost of the car including insurance is the monthly payment, [latex]$410.86[\/latex], plus the monthly cost of the insurance. The insurance cost per month is [latex]\\frac{$2,190}{12}=$182.50[\/latex] since the insurance cost is for [latex]12[\/latex] months. Adding those the cost with insurance is [latex]$593.36[\/latex].\n<\/div>\n<\/div>\n<\/section>\n<h3>Maintaining a Car<\/h3>\n<div class=\"textbox shaded\">\n<p><strong>The Main Idea\u00a0<\/strong><\/p>\n<p>Owning a car involves not just the initial purchase but also ongoing maintenance costs. These can include expenses for fuel, tire replacements, oil changes, windshield wiper replacements, annual inspections, brake pad replacements, and air filter changes. The cost range and frequency of these requirements vary, but all should be included in the budget for owning a car. Additionally, a financial buffer should be kept for unexpected, potentially costly, repairs.<\/p>\n<\/div>\n<section class=\"textbox linkToLearning\" aria-label=\"Link to Learning\">\n<p><a href=\"https:\/\/www.khanacademy.org\/economics-finance-domain\/economics-personal-finance-va\/x3ed8f3aede624754:car-buying\/x3ed8f3aede624754:cost-of-car-ownership\/v\/what-are-the-true-costs-of-car-ownership\" target=\"_blank\" rel=\"noopener\">Watch the video What Are the True Costs of Car Ownership?<\/a> or <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/What+Are+the+True+Costs+of+Car+Ownership_.txt\" target=\"_blank\" rel=\"noopener\">read the transcript of the video here<\/a>.<\/p>\n<\/section>\n<section class=\"textbox example\">Hana needs to budget for her car maintenance. She expects to buy new tires each [latex]5[\/latex] years, which will cost her [latex]$390[\/latex] to replace them all. Oil changes near her cost [latex]$59.99[\/latex], and she believes she will get one every [latex]3[\/latex] months. Her inspection costs [latex]$25[\/latex] per year. Wipers for her car cost [latex]$115[\/latex] for all three and she anticipates changing them every year. She drives less than [latex]30,000[\/latex] miles per year, so she plans to replace the air filter once per year. The air filter for her car costs [latex]$46.25[\/latex]. How much should she budget per month to cover these costs?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160939\">Show Solution<\/button><\/p>\n<div id=\"q160939\" class=\"hidden-answer\" style=\"display: none\">\n[latex]$42.02[\/latex]\n<\/div>\n<\/div>\n<\/section>\n<h3>Fuel Costs<\/h3>\n<div class=\"textbox shaded\">\n<p><strong>The Main Idea\u00a0<\/strong><\/p>\n<p>Fuel efficiency, or gas mileage, is an indicator of how far a vehicle can travel per unit of fuel, generally measured in miles per gallon (MPG). More efficient vehicles consume less fuel to cover a specific distance, thereby reducing fuel costs. Factors influencing fuel efficiency include vehicle size, weight, engine type, driving conditions, and habits. When buying a car, the EPA provides an estimated MPG for city, highway, and combined averages to aid comparisons. Knowing your car&#8217;s typical MPG allows for annual fuel cost calculation.<\/p>\n<\/div>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>annual fuel cost<\/h3>\n<div style=\"text-align: center;\">[latex]\\text{ annual fuel cost } = \\frac{\\text{miles driven annually}}{\\text{miles per gallon}} \\times \\text{ price per gallon of gas}[\/latex]<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\">You&#8217;re deciding between two vehicles. Car J gets [latex]30[\/latex] MPG, and Car K gets [latex]40[\/latex] MPG. If you anticipate driving [latex]12,000[\/latex] miles per year and the price of gas is projected to be [latex]$4.00[\/latex] per gallon, how much would you save in gas costs annually by choosing Car K over Car J?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160940\">Show Solution<\/button><\/p>\n<div id=\"q160940\" class=\"hidden-answer\" style=\"display: none\">\nFirst, we need to determine the annual gas usage for each car:<\/p>\n<ul>\n<li>For Car J, which gets [latex]30[\/latex] MPG: [latex]12,000[\/latex] miles [latex]\u00f7 30[\/latex] MPG [latex]= 400[\/latex] gallons per year<\/li>\n<li>For Car K, which gets [latex]40[\/latex] MPG: [latex]12,000[\/latex] miles [latex]\u00f7 40[\/latex] MPG [latex]= 300[\/latex] gallons per year<\/li>\n<\/ul>\n<p>Then, we can calculate the annual cost of gas for each car:<\/p>\n<ul>\n<li>For Car J: [latex]400[\/latex] gallons [latex]\\times $4.00[\/latex] per gallon [latex]= $1,600[\/latex]<\/li>\n<li>For Car K: [latex]300[\/latex] gallons [latex]\\times $4.00[\/latex] per gallon [latex]= $1,200[\/latex]<\/li>\n<\/ul>\n<p>Therefore, by choosing Car K, which is more fuel-efficient, you would save [latex]$400[\/latex] on gas costs per year given the stated conditions.\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" src=\"\/\/plugin.3playmedia.com\/show?mf=10356040&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=4nrjpa34C1c&amp;video_target=tpm-plugin-dcqhvn0a-4nrjpa34C1c\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Everything+you+need+to+know+about+buying+a+car.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cEverything you need to know about buying a car\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n","protected":false},"author":15,"menu_order":18,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":4885,"module-header":"fresh_take","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/3980"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":51,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/3980\/revisions"}],"predecessor-version":[{"id":15996,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/3980\/revisions\/15996"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/4885"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/3980\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=3980"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=3980"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=3980"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=3980"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}