Question Number 144422 by Engr_Jidda last updated on 25/Jun/21
$${make}\:{n}\:{the}\:{subject}\:{of}\:{the}\:{formular} \\ $$$${if}\:{A}={p}\left(\mathrm{1}+\frac{{r}}{\mathrm{100}}\right)^{{n}} \\ $$
Answered by MJS_new last updated on 25/Jun/21
$${A}={p}\left(\mathrm{1}+\frac{{r}}{\mathrm{100}}\right) \\ $$$$\frac{{A}}{{p}}=\left(\mathrm{1}+\frac{{r}}{\mathrm{100}}\right)^{{n}} \\ $$$$\mathrm{ln}\:\frac{{A}}{{p}}\:=\mathrm{ln}\:\left(\mathrm{1}+\frac{{r}}{\mathrm{100}}\right)^{{n}} \\ $$$$\mathrm{ln}\:\frac{{A}}{{p}}={n}\:\mathrm{ln}\:\left(\mathrm{1}+\frac{{r}}{\mathrm{100}}\right) \\ $$$${n}=\frac{\mathrm{ln}\:\frac{{A}}{{p}}}{\mathrm{ln}\:\left(\mathrm{1}+\frac{{r}}{\mathrm{100}}\right)} \\ $$