Question

By using the formula, find the amount and compound interest on:

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.

Answer 1

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