Question

on what sum of money does the difference between the simple interest and compound interest in 2 years at 5% per annum is 15 rupees​

Answer 1

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\large{\underline{\red{\rm{Given:}}}}$

• The difference between the simple interest and compound interest in 2 years at 5% per annum is 15 rupees

$\large{\underline{\red{\rm{To\:Find:}}}}$

• The sum of money

$\sf{\longrightarrow calculation\:for\:SI}$

$\sf\red{\longrightarrow SI=\dfrac{P*T*R}{100}}$

$\sf{\longrightarrow SI=\dfrac{P*2*5}{100}}$

$\sf{\longrightarrow SI=\dfrac{10P}{100}}$

$\sf{\longrightarrow calculation\:for\:CI}$

$\sf\red{\longrightarrow CI=P(1+\dfrac{r}{100})^n-P}$

$\sf{\longrightarrow CI=P(1+\dfrac{5}{100})^2-P}$

$\sf{\longrightarrow CI=P(\dfrac{105}{100})^2-P}$

$\sf{\longrightarrow CI=P(\dfrac{21}{20})^2-P}$

$\sf{\longrightarrow CI=\dfrac{441P}{400}-P}$

$\sf{\longrightarrow CI=\dfrac{441P-400P}{400}}$

$\sf{\longrightarrow CI=\dfrac{41P}{400}}$

$\sf{\longrightarrow Solving\:CI-SI=15}$

$\sf{\longrightarrow \dfrac{41P}{400}-\dfrac{10P}{100}=15}$

$\sf{\longrightarrow \dfrac{41P-40P}{400}=15}$

$\sf{\longrightarrow \dfrac{41P-40P}{400}=15}$

$\sf{\longrightarrow \dfrac{P}{400}=15}$

$\sf\green{\longrightarrow P=6000}$

Hence,

$\sf\purple{\implies The\:Sum=Rs.6000}$

Answer 2

Step-by-step explanation:

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