Question Number 60441 by ajfour last updated on 21/May/19
$$\mathrm{If}\:\mathrm{a}\:\mathrm{sum}\:\mathrm{of}\:\:\mathrm{money}\:\mathrm{doubles}\:\mathrm{itself} \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{time}\:\mathrm{T},\:\mathrm{when}\:\mathrm{compounded} \\ $$$$\mathrm{continuously},\:\mathrm{find}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{of} \\ $$$$\mathrm{interest},\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{T}. \\ $$
Answered by tanmay last updated on 21/May/19
![A=P(1+(R/(100)))^T A=2P 2P=P(1+(R/(100)))^T (2)^(1/T) =1+(R/(100)) R=100[2^(1/T) −1]](Q60442.png)
$${A}={P}\left(\mathrm{1}+\frac{{R}}{\mathrm{100}}\right)^{{T}} \\ $$$${A}=\mathrm{2}{P} \\ $$$$\mathrm{2}{P}={P}\left(\mathrm{1}+\frac{{R}}{\mathrm{100}}\right)^{{T}} \\ $$$$\left(\mathrm{2}\right)^{\frac{\mathrm{1}}{{T}}} =\mathrm{1}+\frac{{R}}{\mathrm{100}} \\ $$$${R}=\mathrm{100}\left[\mathrm{2}^{\frac{\mathrm{1}}{{T}}} −\mathrm{1}\right] \\ $$
Commented by ajfour last updated on 21/May/19
$$\mathrm{have}\:\mathrm{you}\:\mathrm{assumed}\:\mathrm{annual}\:\mathrm{compounding}, \\ $$$$\mathrm{Sir},\:\mathrm{but}\:\mathrm{i}\:\mathrm{meant}\:\mathrm{continous} \\ $$$$\mathrm{compounding}.. \\ $$
Commented by tanmay last updated on 21/May/19
$${yes}\:{i}\:{could}\:{not}\:{understsnd}.. \\ $$