**Question:**

Find the difference between the simple interest and the compound interest on Rs 5000 for 2 years at 9% per annum.

**Solution:**

Principal amount $=$ Rs. 5000

Simple interest $=$ Rs. $\left(\frac{5000 \times 2 \times 9}{100}\right)=$ Rs. 900

The compound interest can be calculated as follows :

Principal for the first year $=$ Rs. 5000

Interest for the first year $=$ Rs. $\left(\frac{5000 \times 9 \times 1}{100}\right)=$ Rs. 450

Amount at the end of the first year $=$ Rs. $(5000+450)=$ Rs. 5450

Principal for the second year $=$ Rs. 5450

Interest for the second year $=$ Rs. $\left(\frac{5450 \times 9 \times 1}{100}\right)=$ Rs. $490.5$

Amount at the end of the second year $=$ Rs. $(5450+490.5)=$ Rs. $5940.5$

$\therefore$ Compound interest $=$ Rs. $(5940.5-5000)=$ Rs. $940.5$

Now, difference between the simple interest and the compound interest $=($ CI $-$ SI $)=$ Rs. $(940.5-900)=$ Rs. $40.5$