Question Number 8663 by uchechukwu okorie favour last updated on 20/Oct/16
$${if}\:{I}={a}\left(\mathrm{1}−\frac{{r}}{\mathrm{100}}\right)^{{n}} \\ $$$${make}\:{n}\:{the}\:{subject}\:{of}\:{formular} \\ $$$$ \\ $$
Answered by sandy_suhendra last updated on 20/Oct/16
![(1−(r/(100)))^n =(I/a) log (1−(r/(100)))^n = log (I/a) n log(1−(r/(100))) = log (I/a) n = ((log(I/a))/(log (1−(r/(100))))) n = log_((1−(r/(100)))) [(I/a)]](Q8664.png)
$$\left(\mathrm{1}−\frac{\mathrm{r}}{\mathrm{100}}\right)^{\mathrm{n}} =\frac{\mathrm{I}}{\mathrm{a}} \\ $$$$\mathrm{log}\:\left(\mathrm{1}−\frac{\mathrm{r}}{\mathrm{100}}\right)^{\mathrm{n}} =\:\mathrm{log}\:\frac{\mathrm{I}}{\mathrm{a}} \\ $$$$\mathrm{n}\:\mathrm{log}\left(\mathrm{1}−\frac{\mathrm{r}}{\mathrm{100}}\right)\:=\:\mathrm{log}\:\frac{\mathrm{I}}{\mathrm{a}} \\ $$$$\mathrm{n}\:=\:\frac{\mathrm{log}\frac{\mathrm{I}}{\mathrm{a}}}{\mathrm{log}\:\left(\mathrm{1}−\frac{\mathrm{r}}{\mathrm{100}}\right)} \\ $$$$\mathrm{n}\:=\:\mathrm{log}_{\left(\mathrm{1}−\frac{\mathrm{r}}{\mathrm{100}}\right)} \left[\frac{\mathrm{I}}{\mathrm{a}}\right] \\ $$