When Jack started his job working for an industrial manufacturing company, he co

Question

When Jack started his job working for an industrial manufacturing company, he contributed $ 185 at the end of each month into a savings account that earned 3.15 % interest compounded monthly for 6 years. At the end of 6 th year , jack was laid off. To help meet family expenses , Jack withdrew $ 238 from the savings account at the end of each month for 1 year. At the end of the year , Jack found another job and started contributing $ 177 back into the savings account at the end of each month for the next ten years. How much money would he have in the account at the end of the ten years ( after returning to work)? you may use TVM Solver. Show all the necessary work that you need perform to arrive the answer.

Explanation / Answer

The tricky thing on these is when to start and stop. I am assuming that he makes the payment at the end of the sixth year and then starts withdrawing at the end of the first month of the seventh year. 3.15% interest = 3.15%/12 per month = 3.15/12/100 = 0.002625 So each time money has been in the bank one month, we multiply by 1.002625 At the end of the first month he has $185,at the end of the second month he has $185*1.002625 + $185 at the end of the third month he has ($185*1.002625 + $185)*1.002625 +$185 Each month, the sum from the month before is multiplied by the 1.002625 and $185 is added. This is an ideal task for a spreadsheet. at the end of one year, Jack has $2252.333362 at the end of five years he has $12004.85963 at the end of six years he has $14418.00645 Now the formula changes At the end of his first month of unemployment, he has $14418.00645*1.002625 - $238 at the end of the second month of unemployment, he has ($14418.00645*1.002625 - $238)*1.002625 - $238 so, it is the same formula again with -$238 replacing +185 Again, a spreadsheet is perfect for this kind of problem. At the end of his first month of unemplyment, he has $14217.85371. Note that this is not $238 less than he had when he made his last contribution, this is because he earned about $38 in interest, so his account is about $200 less. At the end of his 12 month of unemployment he has $11981.19197 this is $2,436.81 less than he had when he lost his job. Now he has his new job. The first month he earns interest on the $11981.19 and adds the first $177 which comes at the end of the month, so doesn't earn interest yet. This yields $12189.6426 =B85*(1+0.002625)+177 is how it looks on my spreadsheet, where B85 is the cell that contains the $11981.19 balance after his year-long layoff. Again, this formula is the same, except now we have +$177. At the end of his first year at the new job he has $14519.03146 back above what he had when he lost his job. at the end of the fifth he has $25507.78949 At the end of the tenth he has $41338.49714 Of this he contributed $31,704. You can see why savers might go to stocks or higher interest investments.

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