Question

The difference between the compound interest and simple interest on on a certain sum of money at 15% per annum for three years is ₹283.50 find the sum

Answer 1

$\sf\large\underline{Given:}$

$\tt{\implies Difference\:_{(CI-SI)}=Rs.283.50}$

$\rm{\implies Time=3\: years}$

$\rm{\implies Rate=15\%}$

$\sf\large\underline{To\: Find:}$

$\rm{\implies The\:sum=?}$

$\sf\large\underline{Solution:}$

• To calculate difference between ci and si at first we have to find out ci and si separately than subtracting eachother]

$\tt{\implies CI=P\bigg(1+\dfrac{r}{100}\bigg)^n-P}$

$\tt{\implies CI=P\bigg(1+\dfrac{15}{100}\bigg)^3-P}$

$\tt{\implies CI=P\bigg(\dfrac{115}{100}\bigg)^3-P}$

$\tt{\implies CI=P\bigg(\dfrac{23}{20}\bigg)^3-P}$

$\tt{\implies CI=\dfrac{12167P}{8000}-P}$

$\tt{\implies CI=\dfrac{12167P-8000P}{8000}}$

$\tt{\implies CI=\dfrac{4167P}{8000}}$

• Now, calculate SI here]

$\tt{\implies SI=\dfrac{P\times\:T\times\:R}{100}}$

$\tt{\implies SI=\dfrac{P\times\:3\times\:15}{100}}$

$\tt{\implies SI=\dfrac{45P}{100}}$

• Now, calculate difference here]

$\tt{\implies Difference\:_{(CI-SI)}=283.50}$

$\tt{\implies \dfrac{4167P}{8000}-\dfrac{45P}{100}=283.50}$

$\tt{\implies \dfrac{4167P-3600P}{8000}=283.50}$

$\tt{\implies \dfrac{567P}{8000}=283.50}$

$\tt{\implies 567P=2268000}$

$\tt{\implies P=4000}$

$\sf\large{Hence,}$

$\bf{\implies The\:sum=Rs.4000}$

$\rm{\underbrace{Answer-(Rs.4000)}}$