When Jack started his job working at an industrial manufacturing company, he con
ID: 3281945 • Letter: W
Question
When Jack started his job working at an industrial manufacturing company, he contributed $160 at the end of each month into a savings account that earned 3 % interest compounded monthly for 8 years. At the end of the 8th year, Jack was laid off. Fortunately, Jack didn't have to touch the savings account while he was laid off because his wife's income was able to meet the family expenses. After being laid off for one year, Jack found another job (which paid less than his original job) and he started contributing $140 back into the savings account at the end of each month for the next six years. How much money would Jack have in the account at the end of the six years (after returning to work)? You may use the TVM Solver. Show all the necessary work that you need perform to arrive at the answer. The answer should be in the form of a sentence. (15 points) 1. 2. A company with two manufacturing plants, one in Tennessee (T) and the other in Oregon (0), has labor-hour and wage requirements for the manufacture of two inexpensive calculators (model Y and model Z). Each plant has three department used in producing the calculators;they are fabrication (F), assembly (A), and packaging (P). Matrix M represents the labor-hours needed for each model in each department. Matrix N represents the hourly wage for each plant's departments hr 0.100.05 calc.Y calc.Y hr calc.Y hr 0.26 0.21 0.06 calc. Z calc.zl Z 13 $/hr 10$/hr F N- 16 S/hr 1 S/hr A 2 Do the following: A. Interpret m21 in the context of the problem. Your final answer should be in the form of a complete sentence. Be specific. (2 points)Explanation / Answer
1. Since compounding is monthly, 3% interest rate (which is for a year) needs to be converted into monthly rate of 0.25% or 0.0025.
2. A sum P deposited at an interest rate of 0.0025 per month, compounded monthly, amounts at the end of n months to P(1.0025)^n
3. First $160 deposited at the end of first month earns interest for 179 months [8 + 1+ 6 = 15 years or 180 months, but since deposit is made at the end of the month interest eligibility is only for 179 months,] Similarly, second $160 deposited at the end of second month earns interest for 178 months and so on, the last $160 deposited at the end of 96th month (9 years) earns interest for 84 months.
4. Similarly, first $140 deposited at the end of 109th month [8 + 1 = 9 years = 108 months + 1] earns interest for 71 months, second $140 deposited at the end of 110th month earns interest for 70 months and so on, the last $140 deposited at the end of 180th month earns no interest.
Final computation
Thus, the total amount at the end 16 years from start is
{160(1.0025)^191 + 160(1.0025)^190 + ………… + 160(1.0025)^84 } +
{{140(1.0025)^71 + 140(1.0025)^70 + ………… + 140(1.0025)^0 }
= $24432.52+ $11029.12 = $35461.63 ANSWER
Calulate using Geometric Progression
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