A sum of Rs. 10,000 amounts to Rs. 13,225 in 2 years at a certain rate percent per annum, when the interest is compounded annually. What will be the interest (in Rs.) on the same sum for the same time at the same rate, when the interest is compounded 8-monthly?

Let P=10,000, A=13,225, and n=2 years.
Using the compound interest formula for annual compounding:

A=P(1+
100
R
​
)
n

13225=10000(1+
100
R
​
)
2

10000
13225
​
=(1+
100
R
​
)
2

Taking the square root on both sides:

100
115
​
=1+
100
R
​

1+
100
15
​
=1+
100
R
​
⟹R=15% per annum
Now, for compounding 8-monthly over the same time (2 years = 24 months):

Number of periods (n
′
) =
8
24
​
=3 periods

Rate per period (R
′
) = 15%×
12
8
​
=10% per period

Now, compute the new amount (A
′
) with P=10,000, R
′
=10%, and n
′
=3:

A
′
=10000(1+
100
10
​
)
3
=10000×(1.1)
3
=10000×1.331=13310
Compound Interest=A
′
−P=13310−10000=Rs. 3310