Calculate Raises over Time

JLE Campbell

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Dec 1, 2020
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Annual salary increases 50% every 10 years.
If one is earning $81,000 in 2000, in what year did they first earn $24,000.


I tried but am not getting accurate answer.
 
Annual salary increases 50% every 10 years.
If one is earning $81,000 in 2000, in what year did they first earn $24,000.
I tried but am not getting accurate answer.
How do you know that you are not getting accurate answer.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 
I didn't get $24,000, so I could ID year.

Work:. 1990 $81,000×0.5=$40,500
1980 $40,500×0.5=$20,250
 
Solve this: [math](1+i)^{10} = 1.5[/math]
Sorry, not quite paying attention. Better things below.
 
Last edited:
So, sometime between 1980 and 1990.

Your task is to determine just exactly how to calculate those intervening years. Straight line? Probably not. Constant percentage? Maybe.

Solve this: [math](1+i)^{10} = 2[/math]
 
You may also need to rephrase the problem statement.

Does it mean EXACTLY $24,000 or AT LEAST $24,000?
 
Annual salary increases 50% every 10 years.
If one is earning $81,000 in 2000, in what year did they first earn $24,000.

I tried but am not getting accurate answer.
Just to make sure we're understanding you:

Imagine you earned $24,000 in 1950. A 50% increase in 1960 would mean that you make $12,000 more, for a total of $36,000. That is, the salary is multiplied by 1.5 each 10 years.

I didn't get $24,000, so I could ID year.

Work:. 1990 $81,000×0.5=$40,500
1980 $40,500×0.5=$20,250
Here you seem to be supposing that the salary doubles every decade, so that working backward it is halved. (That is, to reverse a multiplication by 2, you divide by 2.) That isn't a 50% increase!

It turns out that if you really use a 50% increase, the answer will be a whole number of decades, and there is no need to interpolate as has been suggested.

How would you reverse a multiplication by 1.5?
 
I didn't get $24,000, so I could ID year.

Work:. 1990 $81,000×0.5=$40,500
1980 $40,500×0.5=$20,250
You are not doing this correctly. Why are you multiply by .5??
Note that if you are making $40,500 in 1990 as you said then you will need to get 100% increase in 10 years to be at 81,000 in 2000! Do you see that??

So what do you multiply the amount in 2000 by to get the correct result for 1990.

The 1st problem is how much do you earn in 1990?? Well if you increase that by 50% you need to get 81,000 which you made in 2000.

So you need to solve for x in 1.5*x = 81000. This value x is what you multiply by to figure out what you made in 1990. What about 1980? ...
 
I didn't get $24,000, so I could ID year.

Work:. 1990 $81,000×0.5=$40,500
1980 $40,500×0.5=$20,250
This is NOT what "50% raise" means!

If, in 1980, the salary was $20,250 then 50% of that is $10,125 so that the new salary, is $20,250+ $10,125= $30,375, not $40,500.

If, at any point, the salary is x then 50% of the salary is 0.50x so that the new salary is x+ 0.50x= 1.50x. The original salary is multiplied by 1.05 so, to go back, you have to divide by 1.5, not 2!
 
[math](1+a)^{10} = 1.5 \land a > 0 \rightarrow a = 0.041379743992410586846[/math]
[math]\dfrac{81000}{(1+a)^{n}} = 24000 \rightarrow n = [/math]??

What does that mean?
 
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