Anil took some loan on simple interest at a certain rate and paid ₹12,800 as interest after 2 years. His friend Sumit also borrowed the same sum on compound interest for the same period and same rate of interest compounded annually and paid ₹704 more interest than that paid by Anil. What is the rate of interest per annum?

For simple interest (SI), the interest earned is the same every year.
Anil paid a total simple interest of ₹12,800 over 2 years.

Therefore, the Simple Interest for 1 year is:

SI
1
​
=
2
12800
​
=₹6,400
For compound interest (CI), the difference between CI and SI for 2 years is equal to the interest earned in the second year on the first year's interest.

Given that Sumit paid ₹704 more interest than Anil:

CI−SI=₹704
This ₹704 is the interest calculated on the first year's interest (SI
1
​
) at the annual rate of interest R.

704=R% of SI
1
​

704=
100
R
​
×6400
704=64×R
R=
64
704
​
=11%
Thus, the rate of interest per annum is 11%.