maria.pilar
New member
- Joined
- Mar 3, 2015
- Messages
- 3
Hi everyone! Could you please help me find the "smart" and "short" solution to this problem? Step by step would be useful. I can solve it the long way, but I am looking for a quicker path. Thanks!
I buy a car for $8,000. I will use my monthly wages to pay for it.
At the end of this month I will earn $1,000.
My wages will increase by 5% every month.
In how many months will my car be completely paid off?
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So the long way would be to add the monthly wages until the total is at least $8,000:
1,000 + 1,000*1.05 + 1,000*1.05*1.05 + 1,000*1.05*1.05*1.05.... => 8,000
OR
1,000 + 1,000*1.05 + 1,000*1.05^2 + 1,000*1.05^3... => 8,000
The answer is 7 months, which add to 8,142.87 - but it is long and tedious to add these results until we reach 8,000.
I can see that we are dealing with the same base, 1.05.
I tried simplifying the equation but my method does not work because n is unknown:
1,000 (1 + 1.05 + 1.05^2 + 1.05^3...) => 8,000
I also tried another manner, which did not work either when applying it to different cases:
1,000x + 1,000*1.05^x => 8,000
1,000x + 1,000*xln1.05 => 8,000
All your help is appreciated
I buy a car for $8,000. I will use my monthly wages to pay for it.
At the end of this month I will earn $1,000.
My wages will increase by 5% every month.
In how many months will my car be completely paid off?
-----
So the long way would be to add the monthly wages until the total is at least $8,000:
1,000 + 1,000*1.05 + 1,000*1.05*1.05 + 1,000*1.05*1.05*1.05.... => 8,000
OR
1,000 + 1,000*1.05 + 1,000*1.05^2 + 1,000*1.05^3... => 8,000
The answer is 7 months, which add to 8,142.87 - but it is long and tedious to add these results until we reach 8,000.
I can see that we are dealing with the same base, 1.05.
I tried simplifying the equation but my method does not work because n is unknown:
1,000 (1 + 1.05 + 1.05^2 + 1.05^3...) => 8,000
I also tried another manner, which did not work either when applying it to different cases:
1,000x + 1,000*1.05^x => 8,000
1,000x + 1,000*xln1.05 => 8,000
All your help is appreciated