Question

if the difference between compound interest and simple interest on a certain amount for 2 years at 10% annum compounded annually is Rupees 100.5 then find the principal amount

Answer 1

Dear Student,
$$\begin{gathered} lettheprincipalamountbep \\ r=10\% \\ t=2years \\ Simpleinterest=\frac{p\times r\times t}{100} \\ compundinterest=p(1+\frac{r}{100}{)}^t-p \\ Accordingtoquestion: \\ Differencebetweencompoundinterestandsimpleinterest=Rs100.5 \\ p(1+\frac{r}{100}{)}^t-p-\frac{p\times r\times t}{100}=100.5 \\ p(1+\frac{10}{100}{)}^2-p-\frac{p\times 10\times 2}{100}=100.5 \\ p{\left(1.1\right)}^2-p-\frac{p}{5}=100.5 \\ p({\left(1.1\right)}^2-1-0.2)=100.5 \\ p(1.21-1-0.2)=100.5 \\ p(0.01)=100.5 \\ p=\frac{100.5}{0.01} \\ p=10,050 \\ PrincipalamountisRs10,050 \end{gathered}$$

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