Question

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 Yı, 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)

Answer 1

Answer to Qs.1

Jack invested $220 per month at interest rate of 2.5% compounded monthly for 8 years. So, total amount at the end of 8 years comes to $ 23,354.52. (using TVM solver)

After 8 years Jack was laid off and withdraw $300 per month for 2 years. Total with draw by Jack during 2 year including loss on interest comes to $ 7376.22

Also $23354.22 at the end of 10^th year will become = P(1+r / n)^tn = 23354.22 (1+0.025/12)^12*2 = 24575.24

After 10 years, Jack is left with $24575.24 - $7376.22 = $17199.02.

After 10 years, Jack invested $150 per month for 6 years and principal amount already invested was 17199.02, so final amount at the end of 6 yr post employment will be $31618.31

1. At the end of the six years post-employment, Jack will have = $31618.31 in the account.
2. Total Interest that Jack earned during 6 years would be = $31618.31 – [220*8*12+150*6*12-300*2*12] = $ 31618.31 – 24720 = $6898.31