Question 208034: Suppose you are offered two jobs. One pays $30,000 the first year with annual raises of $2000 each year. The second offers a starting salary of $27,000 and raises of 8% each year. At the end of ten years, what would your yearly salary be from a) the first job? b)the second job?
My answer; $30,000=1 year + $2000=each coming year * 10 years
but since the first year is already given I dont have to count it with do I? (thats why I am not sure if I got this right)
a) 2000*9=18,000 30,000+18,000=48,000 so $48,000 after 10 years
b)27,000=1 year + 8% each coming year * 10 years
(here again I only put 9 years to count, since 27,000 already is the first year, or is that wrong?)
270*8=2,160 2,160*9=19,440 27,000+19,440=46,440 so $46,440 after 10 years
Could someone please tell me if I solved the problem right?
Found 2 solutions by Theo, rapaljer:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Suppose you are offered two jobs. One pays $30,000 the first year with annual raises of $2000 each year. The second offers a starting salary of $27,000 and raises of 8% each year. At the end of ten years, what would your yearly salary be from a) the first job? b)the second job?
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If we assume that the salary increase is at the end of each year, we get the following:
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first job would be $30,000 + (10 * $2,000) = $50,000
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second job would be $27,000 * (1.08)^10 = $58,290.97
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If we assume that the salary increase is at the beginning of each year, we get the following:
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first job would be $30,000 + (9 * $2,000) = $48,000
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second job would be $27,000 * (1.08)^9 = $53,973.12
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It doesn't really matter whether you used 9 years or 10 years
because you will be making more money at the second job either way.
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They are asking:
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At the end of ten years, what would your yearly salary be from a) the first job? b)the second job?
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This is nebulous and clearly open to interpretation. They do not clearly state when you get the annual salary increase.
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In a real world situation you would have had to ask for a clarification as to they wanted you to make the calculations.
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your answer should include:
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if they get a raise at the end of each year, then at the end of the 10th year the annual salary would be.
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your alternate answer should include:
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if they get a raise at the beginning of the next year, then at the end of the 10th year, the annual salary would be.
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in the first case, carrying out the operations 10 years would be correct.
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in the alternate case, carrying out the operations 9 years would be correct.
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when you do the 8% solution, you are doing compound interest, not simple interest.
simple interest would be $27,000 + (.08*10*27000)
compound interest would be $27,000 * (1.08)^10 as shown.
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first proposal yearly salary with raises at the end of each year would look like this.
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end of year 1: $32,000
end of year 2: $34,000
end of year 3: $36,000
end of year 4: $38,000
end of year 5: $40,000
end of year 6: $42,000
end of year 7: $44,000
end of year 8: $46,000
end of year 9: $48,000
end of year 10: $50,000
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first proposal yearly salary with raises at the end of each year would look like this.
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end of year 1: $30,000
end of year 2: $32,000
end of year 3: $34,000
end of year 4: $36,000
end of year 5: $38,000
end of year 6: $40,000
end of year 7: $42,000
end of year 8: $44,000
end of year 9: $46,000
end of year 10: $48,000
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he doesn't get $50,000 until the beginning of the 11th year.
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same concept applies for the 8% case.
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Without knowing, you need to qualify your answer as I indicated and I would think you need to show both answers with the qualification for each.
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My answer would be:
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If the salary increases at the end of each year, then:
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first job would be paying $30,000 + (10 * $2,000) = $50,000 and the second job would be $27,000 * (1.08)^10 = $58,290.97
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If the salary increases at the beginning of each year, then:
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first job would be paying $30,000 + (9 * $2,000) = $48,000 and the second job would be $27,000 * (1.08)^9 = $53,973.12
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Answer by rapaljer(4671)  (Show Source):
You can put this solution on YOUR website! I think in either case, you would use 10 for the time of the salary instead of 9. At the end of the first year, you would have a $2000 raise, at the end of the 10th year, you would have 10 $2000 raises or $20,000, so your salary would be $30,000 + $20,000= $50,000.
The second would be using a formula for compound interest
Use a calculator:
R^2
Dr. Robert J. Rapalje
Seminole State College
Altamonte Springs, FL 31714
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