Question

An amount is given at an interest of $5\%$ per annum. Find the amount if the difference of compound and simple interests for $2$ yrs is Rs. $6$.

Answer 1

Given interest is $5$% p.a Difference between compound and simple interest is Rs. $6$

Let the principal amount be $P$

simple interest $=2\times \frac{5}{100}P=\frac{P}{10}$

Compound interest after 1 year $=\frac{P}{20}$

so compound interest after 2 years $=(P+\frac{P}{20})\times \frac{1}{20}=\frac{21P}{400}$

total compound interest $=\frac{P}{20}+\frac{21P}{400}=\frac{41P}{400}$

$\Rightarrow \frac{41P}{400}-\frac{P}{10}=6\Rightarrow \frac{P}{400}=6\Rightarrow P=Rs.2400$