How to find n? `50000xx0.05xxn + 50000 lt 50000xx(1.035)^n`

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thilina-g | College Teacher | (Level 1) Educator

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`50000xx0.05xxn + 50000 lt 50000xx(1.035)^n`

Divide both sides by 50000

I can write this as,


I can use the binomial expansion to expand the left side.


`0.035n+(n(n-1))/2xx0.035^2+(n(n-1)(n-2))/6 xx 0.035^3gt0.05n`

Multiply by 6 and divide by `0.035^3` .





`n(n-21.0554)(n+103.7655)gt0` ` `



So the inequality doesn't exist.` `



The inequality is exists.

`0 ltnlt 21.0554`


So the inequality doesn't exist.



The inequality is exists.


Therefore we have two ranges of solutions.





Actually this is an approximate answer, you can increase the accuracy by increasing the terms of binomial expansion.