When Jack started his job working at an industrial manufacturing company, he con
ID: 3121318 • Letter: W
Question
When Jack started his job working at an industrial manufacturing company, he contributed $165 at the end of each month into a savings account that earned 3.25 % interest compounded monthly for 9 years. At the end of the 9^th 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 two years. Jack found another job (which paid less than his original job) and he started contributing $132 back into the savings account at the end of each month for the next five years. How much money would Jack have in the account at the end of the five 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.Explanation / Answer
Preparatory work
1. Since compounding is monthly, 3.25% interest rate (which is for a year) needs to be converted into monthly rate of 0.2708% or 0.002708.
2. A sum P deposited at an interest rate of 0.002708 per month, compounded monthly, amounts at the end of n months to P(1.002708)n
3. First $165 deposited at the end of first month earns interest for 191 months [9 + 2+ 5 = 16 years or 192 months, but since deposit is made at the end of the month interest eligibility is only for 191 months,] Similarly, second $165 deposited at the end of second month earns interest for 190 months and so on, the last $165 deposited at the end of 108th month (9 years) earns interest for 84 months.
4. Similarly, first $132 deposited at the end of 133rd month [9 + 2 = 11 years = 132 months + 1] earns interest for 59 months [5 years or 60 months - 1), second $132 deposited at the end of 134th month earns interest for 58 months and so on, the last $132 deposited at the end of 192nd month earns no interest.
Final computation
Thus, the total amount at the end 16 years from start is
{165(1.002708)191 + 165(1.002708)190 + ………… + 165(1.002708)84 } +
{{132(1.002708)59 + 132(1.002708)58 + ………… + 165(1.002708)0 }
= 25938.28 + 9312.86 = 35251.14 ANSWER
[Note: the above two series within {} are Geometric Progression and the sums have been found using the formula for GP sum using Excel Function]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.