solve for r without using a scientfic calculator : 25000 = 150* (r^120 - 1) / (r-1)   Thank you  I dont have a scientific calculator. Show me all your steps please .

1 Answer

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embizze | High School Teacher | (Level 2) Educator Emeritus

Posted on

I really don't think you have given all of the information for the problem.

As stated, you have apparently been given that the first term of a geometric series is 150 and that the sum of the first 120 terms is 25000 and you are asked to find r, the common ratio.

`25000=150(r^120-1)/(r-1)` Divide both sides by 150:

`500/3=(r^120 -1)/(r-1)`  Use the means-extremes product property

`500r-500=3r^120-3` Rewrite in standard form:

`3r^120-500r+497=0`

I do not know of a simple way to solve this. It will not factor. Perhaps you could use guess and check with a basic 4-function calculator, but it will take you awhile. Using a graphing calculator (a spreadsheet application will do also) the approximate answer for r is `r~~1.00526`

Check: `150(1.00526^120-1)/(1.00526-1)`

`~~150(.876757854/.00526)=150(166.6840027)=25002.6`

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Is the original problem an annuity problem? (Make $150 payments monthly for 10 years -- what rate gives a total of $25000?) Easiest to solve with a TVM (time value of money) solver on a graphing calculator or in a spreadsheet.

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If you don't have a scientific calculator, there are many emulators on the internet. If you are not allowed to use them, this is an almost impossible problem. Time consuming at the very least.