resentation, Neatness, and Organization points (5 points) The recitation instructors will be giving yo score (out of 5 points) that reflect how well your presentation, neatness, and organization of your lutions are 1. When Jack started his job working for an industrial manufacturing company, he contributed $220 at the end of each month into a savings account that earned 2.5 % interest compounded monthly for 8 years. At the end of the 8th year, Jack was laid off. To help meet family expenses Jack withdrew $300 from the savings account at the end of each month for 2 years. At the end of the second year of being unemployed, Jack found another job and started contributing $150 back into the savings account at the end of each month for the next six years. Do the following: A. How much money would he have in the account at the end of the six years (after returning to work)? Use the TVM Solver to solve this problem. Show all the necessary work that you need perform to arrive at the answer. (12 points) Determine the total interest that Jack earned during the 16 years of the account. (12 points 2. The Shiver-me-Timbers tree farms has 6,500 lumber-quality trees ready to be harvested. The company has a strategy of harvesting 19% of the trees that are remaining at the beginning of the year) and planting 120 lumber-quality trees during the year. Let n represent the number of years and yn represent the number of lumber-quality trees on the farm at the end of the year. Do/answer the following: A. Form the difference equation (and initial value) that models the timber company's strategy where y, represent the number of lumber-quality trees on the farm at the end of the year and you represent the number of lumber-quality trees on the farm at the end of the previous year. (5 points) B. Use the difference equation to generate Y, y, and ys. Round the values of y., y, and y, to two decimal places. Show how you arrived at your answers. (3 points) C. Solve the difference equation. Show in detail how you arrived at your a w in detail how you arrived at your answer. (5 points) D. Check to see if your solution of the difference equation is correct by generating Y and y using the solution of the difference equation. Round the values of yz and y, to two decimal places. Show how you arrived at your answers. (2 points) E. Now that you have checked to see if your solution of the difference equation is the correct solution of the difference equation, now use it to generate the values for yo. Yo Yo Yo V100, and yuso. Round the resulting values to two decimal places. (3 points) F. Do the values from part E surrest that there will be a time when all the trees on the farm will all be harvested (i.e. will there be a time in which there will no longer be any trees to harvest on the farm)? Explain (2 points) G. If you have correctly completed the above parts, then you should notice something when you look at the values of 10o and Yuso in part E and look at the work you did in part to solve the difference equation. What do you notice? (2 points) 3. The quantity demanded each month for an Oh-So-Good coffee maker is 400 when the unit price is $50; the quantity demanded each month is 150 when the unit price is $80. The supplier will market 800 of the Oh So Good coffee maker if the unit price is $56. At a unit price of S80, the supplier is willing to market 1,500 units. Both the demand and supply equations are known to be linear. Using the variables q (for quantity) and p (for price, in dollars), do the following: A. Determine the demand equation. Show the steps that you performed to arrive at your answer. Place a box around your final answer. (5 points) B. Determine the supply equation. Show the steps that you performed to arrive at your answer. Place a box around your final answer. (5 points) Without any of the graphing functions, matrix functions, or solving functions in the calculator, determine the equilibrium quantity and price. Show the steps that you performed to arrive at your answer. Your final answer should be in the form of a complete sentence. (5 points) 4. WITHOUT the use of the TVM Solver, use an appropriate formula to determine the annual interest rate of an account if the account earns interest monthly and $40,234.23 grows to $42294.88 in two years. No money is deposited or withdrawn during the two years. Show, in detail, how you arrive at your answer. Show intermediate steps that clearly indicate that you did not use the TVM Solver. (5 points) Credit Problem: - WITHOUT the use of the TVM Solver, determine how much money you need to deposit into a newly opened account (in which no money was initially deposited) at the end of each month fo the next 5 vears in order to earn a total of $486.51 in interest during the 5 years. The account earns 2.25% interest compounded quarterly. Show, in detail, how you arrive at your answer. Show intermediate steps that clearly indicate that you did not use the TVM Solver. (3 points) A couple has decided to start a college educational trust fund for their new born daughter. Suppose a couple deposited an initial $15,000 into the account on the child's actual date of birth and then for the next 10 years, on the day before her birthday, they make a deposited $6,000 into the account. After the tenth year, the couple stopped depositing money into the account. When their daughter goes off to college, the trust fund will pay her R dollars on her 18th, 19th, 20th, and 21st birthday. Use the TVM solver to help determine the value of Rif the money earns 1.85% interest compounded annually. Show in detail how you arrived at your answer. Your final answer should be in the form of a sentence. Write short comments in your solution that describe the steps that you use to solve this problem. Note: There is one small, but very important detail that you need to determine that will determine if you calculate the correct answer or not; so think about each step very carefully. (3 points)
