Question

Compound interest on a certain sum of money at the rate of 5% becomes rupees 1537.50 in 2 years. Find the simple interest on same sum for same time at same rate interest.

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Compound interest for 2 years is Rs.1537.50}$

$\mathsf{and\;rate\;of\;interest\;is\;5\%}$

$\underline{\textsf{To find:}}$

$\textsf{Simple interest for the same sum of money}$

$\underline{\textsf{Solution:}}$

$\textsf{We apply copound interest formula}$

$\boxed{\mathsf{Compound\;interest=P\left(1+\dfrac{r}{100}\right)^n-P}}$

$\mathsf{Compound\;interest\;for\;2\;years=Rs.1537.50}$

$\mathsf{P\left(1+\dfrac{r}{100}\right)^2-P=1537.50}$

$\mathsf{P\left(1+\dfrac{5}{100}\right)^2-P}=1537.50}$

$\mathsf{P\left(1+\dfrac{1}{20}\right)^2-P=1537.50}$

$\mathsf{P\left(1+\dfrac{1}{400}+\dfrac{2}{20}\right)-P=1537.50}$

$\mathsf{P+\dfrac{P}{400}+\dfrac{P}{10}-P=1537.50}$

$\mathsf{\dfrac{P}{400}+\dfrac{P}{10}=1537.50}$

$\mathsf{\dfrac{P+40P}{400}=1537.50}$

$\mathsf{\dfrac{41\,P}{400}=1537.50}$

$\mathsf{P=1537.50{\times}\dfrac{400}{41}}$

$\mathsf{P=153750{\times}\dfrac{4}{41}}$

$\mathsf{P=3750{\times}4}$

$\mathsf{P=Rs.\,15000}$

$\textsf{Simple interest for 2 years}$

$\mathsf{=\dfrac{P\,n\,r}{100}}$

$\mathsf{=\dfrac{15000{\times}2{\times}5}{100}}$

$\mathsf{=\dfrac{15000{\times}10}{100}}$

$\mathsf{=150{\times}10}$

$\mathsf{=Rs.\,1500}$

$\underline{\textsf{Answer:}}$

$\textsf{Simple interest for 2 years is Rs. 1500}$

$\underline{\textsf{Find more:}}$

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Answer 2

hope this helps you

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