Question

The simple interest and the compound interest on a certain sum for 2 years is Rs 1250 and Rs 1475, respectively. Find the rate of interest.

Answer 1

Dear student,

$$\begin{gathered} LetthePrincipalbeP \\ andRateofinterestbeR\% \\ WeknowSI=\frac{PRT}{100} \\ \Rightarrow 1250=\frac{P\times R\times 2}{100} \\ \Rightarrow \frac{1250\times 100}{2}=PR \\ \Rightarrow 1250\times 50=PR \\ \Rightarrow \frac{62500}{P}=R--\left(1\right) \\ Also,CI=A-P \\ \Rightarrow CI=P{\left(1+\frac{R}{100}\right)}^t-P \\ \Rightarrow 1475=P{\left(1+\frac{62500}{P\times 100}\right)}^2-P \\ \Rightarrow 1475=P{\left(1+\frac{625}{P}\right)}^2-P \\ \Rightarrow 1475=P\left(1+\frac{390625}{P^2}+\frac{1250}{P}\right)-P--[u\sin g{\left(a+b\right)}^2=a^2+b^2+2ab] \\ \Rightarrow 1475=P+\frac{390625}{P}+1250-P \\ \Rightarrow 1475=\frac{390625}{P}+1250 \\ \Rightarrow 1475-1250=\frac{390625}{P} \\ \Rightarrow 225=\frac{390625}{P} \\ \Rightarrow P=\frac{390625}{225} \\ \Rightarrow P=Rs1736.11 \\ puttingthisvaluein\left(1\right)weget \\ R=\frac{62500}{1736.11} \\ =36\% \\ thusthevalueRis36\%respectively. \end{gathered}$$
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