Algebra 2: Lesson 11-9 Calculating Monthly Payments. Learning Goal: 1) How do we determine a monthly payment for a loan using any given formula?
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1 NAME: DATE: Algebra 2: Lesson 11-9 Calculating Monthly Payments Learning Goal: 1) How do we determine a monthly payment for a loan using any given formula? Warm Up: Ready? Scenerio. You are 25 years old and hold a steady job. One day on the way to work, you see that your dream car is on sale at a car dealership. You go to the dealer to see about buying it. The car dealer tells you that he has this great deal on the car. Apparently, only for today, he is selling the car for $45,000 with a down payment of $3,000. He says he did some calculations and gives you three car loan options which are shown below. Loan 1 -month loan at Loan 2 -month loan at Loan 3 -month loan at What will be the monthly payments for each option? Which will you take it? Can you afford any of them? If you end up buying it, how much spending money will you have left over each month for each option? How much will you end up paying back (with interest) after the loan is paid off? Is there a better deal out there? Since we are talking math here, there definitely is a better way to figure all this out than just signing the agreement and hoping for the best. Many people take out a loan to purchase a car and then repay the loan on a monthly basis. Today we will figure out how banks determine the monthly payment for a loan in today s class. As seen in the scenario above, when deciding to get a car loan, there are many things to consider. For car loans, a down payment is a very common requirement. A down payment is the amount of money the person will pay towards the cost of the car before the loan is taken. For example: For the scenario above, he is selling the car for $45,000 with a down payment of $3,000. What will the loan amount be if he decides to choose one of the three loan options?
2 When calculating loans and monthly payments, there are a few different formulas that can be used. The formula used depends on the type of loan and what is included in the loan. Below are some examples of monthly loan formulas. ( ( ( ) ) ) ( ) ( ) M is the mortgage payment P is the principal amount of the loan r is the monthly interest rate N is the number of monthly payments ( ) M = monthly payment P = amount borrowed r = annual interest rate n = number of monthly payments Tips when working with monthly loan formulas: Read the question twice. Be sure to pay attention to what each variable stands for. The second time, write down the numbers that correspond to each variable. Determine the variable that they are asking you to find. Substitute the values in the given formula. Try to simplify any expressions within the formula before solving for the remaining variable. If you are solving for an exponent, you will have to use logs. A down payment is the amount you would pay prior to taking out a loan. This amount gets subtracted from the total purchase price. 1. Jim is looking to buy a vacation home for $172,600 near his favorite southern beach. The formula to compute a mortgage payment, M, is where P is the principal amount of the loan, r is the monthly interest rate, and N is the number of monthly payments. Jim's bank offers a monthly interest rate of 0.305% for a 15-year mortgage. With no down payment, determine Jim's mortgage payment, rounded to the nearest dollar.
3 Question #1 continued Jim is looking to buy a vacation home for $172,600 near his favorite southern beach. The formula to compute a mortgage payment, M, is where P is the principal amount of the loan, r is the monthly interest rate, and N is the number of monthly payments. Jim's bank offers a monthly interest rate of 0.305% for a 15-year mortgage. Algebraically determine the fewest number of whole months that Jim needs to make in order for his mortgage payment to be no more than $1100.
4 2. Using the formula below, determine the monthly payment on a 3-year car loan with a monthly percentage rate of 0.75% for a car with an original cost of $25,000 and a $2000 down payment, to the nearest cent. ( ( ( ) ) ) The affordable monthly payment is $350 for the same time period. Determine an appropriate down payment, to the nearest dollar.
5 3. Monthly mortgage payments can be found using the formula below: ( ) ( ) ( ) M = monthly payment P = amount borrowed r = annual interest rate n = number of monthly payments The Banks family would like to borrow $120,000 to purchase a home. They qualified for an annual interest rate of 4.8%. Algebraically determine the fewest number of whole years the Banks family would need to include in the mortgage agreement in order to have a monthly payment of no more than $720.
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