On a certain principal if the Simple Interest for two years is $\text{Rs }3000$ and Compound Interest for the two years is $\text{Rs }3225$, what is the rate of Interest?

Given:Simple Interest for 2 years (${\text{SI}}_2$) = $\text{Rs }3000$ Compound Interest for 2 years (${\text{CI}}_2$) = $\text{Rs }3225$ Since simple interest is distributed equally across each year, the Simple Interest for the first year is:
$${\text{SI}}_1=\frac{3000}{2}=\text{Rs }1500$$
The difference between Compound Interest and Simple Interest for 2 years is the interest earned on the first year's interest:
$${\text{CI}}_2-{\text{SI}}_2=3225-3000=\text{Rs }225$$
This difference of $\text{Rs }225$ is the interest calculated on the first year's interest of $\text{Rs }1500$.Therefore, the rate of interest ($R$) is:
$$R=\left(\frac{225}{1500}\right)\times 100\%$$
$$R=\frac{225}{15}\%=15\%$$