 # The difference between the compound interest and the simple interest on a certain sum for 3 years at 10% per annum is Rs 93.

Question:

The difference between the compound interest and the simple interest on a certain sum for 3 years at 10% per annum is Rs 93. Find the sum.

Solution:

Let $P$ be the sum.

Then SI $=$ Rs $\left(\frac{P \times 3 \times 10}{100}\right)=$ Rs $\frac{30 P}{100}=$ Rs $\frac{3 P}{10}$

Also, CI $=$ Rs. $\left\{P \times\left(1+\frac{10}{100}\right)^{3}-P\right\}$

$=$ Rs. $\left\{P \times\left(\frac{100+10}{100}\right)^{3}-P\right\}$

$=$ Rs. $\left\{P \times\left(\frac{11}{10}\right)^{3}-P\right\}$

$=$ Rs. $\left\{\left(\frac{1331 P}{1000}\right)-P\right\}$

$=$ Rs. $\left\{\frac{1331 P-1000 P}{1000}\right\}$

$=$ Rs. $\frac{331 P}{1000}$

Now, $($ CI $-$ SI $)=$ Rs $\left(\frac{331 P}{1000}-\frac{3 P}{10}\right)$

$=$ Rs $\left(\frac{331 P-300 P}{1000}\right)$

$=$ Rs $\frac{31 P}{1000}$

Now, Rs. $93=\frac{31 P}{1000}$

$\Rightarrow P=\left(\frac{93 \times 1000}{31}\right)=$ Rs. 3000

Hence, the required sum is Rs. 3000 .