Unit Activity Unit: Single-Variable Expressions, Equations and Inequalities This activity will help you meet these educational goals: Mathematical Practices You will make sense of problems and solve them, use mathematics to model real-world situations, and use appropriate tools strategically. Introduction Have you ever made a mistake when trying to solve a math problem? It can be pretty easy to do, and often will result in losing points on an exam. In the real world, such mistakes can have more serious effects: Miscalculating how much gas you have left in your car will leave you stranded. Miscalculating how much money you have left in your bank account might cost you an overdraft fee. Even more serious, miscalculations have resulted in serious accidents happening many times. Once, as a result of not using the correct units, a satellite sent to Mars burned up in the atmosphere, wasting over $300 million dollars. Fortunately, there are steps you can take to help avoid making errors along the way. One of these strategies is manipulating formulas so they are solving for the variable you want before you substitute values for the variables in the formula. This technique is especially useful when working with large, unwieldy numbers. __________________________________________________________________________ Directions and Analysis Task 1: Interest in Finance Interest is a concept familiar to most people: every credit card in existence has a term called annual percentage rate (APR), which is an interest rate. Suppose you charged $1,000 to a credit card that has a minimum payment each month equal to the interest owed. Can you figure out how much the interest rate is based on this amount? The formula for simple interest is where I is the amount you will pay in interest, r is I r P m, the rate at which interest will accrue, P is the principal (amount borrowed), and m is the number of times the interest is applied. a. To solve for the interest rate of your credit card, you need to understand which variables in the above formula you have. If your minimum monthly payment is $22 on the $1,000 credit card bill, which variables do you know the values of? Type your response here: 1 2015 EDMENTUM, INC. b. Manipulate the formula so it will calculate the interest rate you are paying instead of the amount of money you are paying. Type your response here: c. Now that you have a formula that will give you the interest rate, plug in the values for the problem and solve for that interest rate. Interest rates are usually represented for a time period: over what time period does this rate apply? What would the interest rate be if it were a yearly rate? Type your response here: d. Now consider a different situation. Payday loans are a type of loan where you can get money for a future paycheck, typically two weeks in advance. A typical payday loan service might charge $15 for a loan against a paycheck you will receive in two weeks. The interest rate is 10% of the paycheck over that two-week period. Given this information, which variables in the interest formula are known? Develop a formula that will solve for the unknown variable. Type your response here: e. Solve for the value of the unknown variable. Type your response here: __________________________________________________________________________ Resources Document any references you used for this project below. At minimum, include a title and URL for any Internet resource: 2 Evaluation Your teacher will use this rubric to evaluate the completeness of your work as well as the clarity of thinking you exhibit. Total Points: 5 Task 1: Interest in Finance Task points: [5] a. Identifying known variables 1 b. Manipulating the formula to solve for the desired variable c. Determining yearly interest rate 1 1 d. Manipulating the formula for a new situation 1 e. Calculating a paycheck based on a payday loan interest rate and interest amount 3 1