The difference between the compound interest and the simple inter…

Question

The difference between the compound interest and the simple interest on a certain sum for 2 years at 6% per annum is Rs. 90. Find the sum.

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Answer

Difference between C.I and S.I. = Rs. 90 Rate (R) = 6% p.a Period (n) = 2 years Let principal (P) = Rs. 100 $\therefore$ Amount on C.I $=\text{P}\Big(1+\frac{\text{R}}{100}\Big)^{\text{n}}$ $=100\Big(1+\frac{6}{100}\Big)^2$ $=\text{Rs. }100\times\Big(\frac{53}{50}\Big)^2$ $=\text{Rs. }100\times\frac{53}{50}\times\frac{53}{50}=\text{Rs. }\frac{2809}{25}$ $\therefore\text{C.I}=\text{A}-\text{P}=\text{Rs. }\frac{2809}{25}-100$ $=\text{Rs. }\frac{2809-2500}{25}=\frac{309}{25}$ and S.I $=\frac{\text{PRT}}{100}=\frac{100\times6\times2}{100}=\text{Rs. }12$ Difference between C.I and S.I. $=\text{Rs. }\frac{309}{25}-12$ $\text{Rs. }\frac{309-300}{25}=\frac{9}{25}$ Now if difference is $\text{Rs. }\frac{9}{25}$ then Principal = Rs. 100 and if difference is Rs. 90, then principal$=\frac{100\times25\times90}{9}=\text{Rs. }25000$

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