Question

The compound interest on a sum of money for $2$ years is Rs $410$ and the simple interest on the same sum for the same period and at the same rate is Rs. $400$. Find the rate of interest.

Answer 1

Since, simple interest earned in 2 years is $Rs.400$

Therefore, interest earned in 1 year $=\frac{400}{2}=Rs.200$ [Since, SI is same for every year]

Also, SI and CI in 1st year is same.

Therefore, CI in1 year $=Rs.200$

Thus, CI in 2nd year $=Rs.410-200=Rs.210$

Therefore the difference of CI in 2 years $=Rs.10$

This interest was earned on the interest of 1st year.

Therefore, $R=\frac{\text{Interest earned}}{\text{Interest earned upon}}\times 100\%$

$=\frac{10}{200}\times 100\%$

$=5\%$