Question

Find the sum that yields an interest of ?170 after two years at the rate of 12.5% p.a. interest being compounded annually.

Answer 1

Dear student,
$$\begin{gathered} CI=Rs170 \\ Time=2years \\ Rate=12.5\% \\ weknowCI=A-P \\ \Rightarrow 170=P{\left(1+\frac{12.5}{100}\right)}^2-P \\ \Rightarrow 170=P\left[{\left(1+\frac{12.5}{100}\right)}^2-1\right] \\ \Rightarrow 170=P\left[{\left(1+\frac{125}{1000}\right)}^2-1\right] \\ \Rightarrow 170=P\left[{\left(1+\frac{1}{8}\right)}^2-1\right] \\ \Rightarrow 170=P\left[{\left(\frac{9}{8}\right)}^2-1\right] \\ \Rightarrow 170=P\left[\left(\frac{81}{64}\right)-1\right] \\ \Rightarrow 170=P\left[\frac{81-64}{64}\right] \\ \Rightarrow 170=P\left[\frac{17}{64}\right] \\ \Rightarrow \frac{170\times 64}{17}=P \\ \Rightarrow 10\times 64=P \\ \Rightarrow \boxed{P=Rs640} \\ ThustherequiredsumisRs640 \end{gathered}$$
Regards