What is the difference between the compound interest on a sum of ₹10,000 at 12% p.a. for 1
4
1
​
years when the interest is compounded annually and when the interest is compounded 5-monthly? (nearest to a ₹)

Given:
Principal (P) = ₹10,000
Rate (R) = 12% p.a.
Time (T) = 1
4
1
​
 years=
4
5
​
 years=
4
5
​
×12=15 months

Case 1: Compounded Annually
The time is 1 year 3 months.

Amount after 1st year = 10000×(1+
100
12
​
)=11200

Interest for the remaining 3 months (3/12=1/4 year) on ₹11,200:

Interest=11200×12%×
4
1
​
=11200×3%=336
Total Amount (A
1
​
) = 11200+336=11536

CI
1
​
=11536−10000=₹1,536

Case 2: Compounded 5-Monthly

Number of periods (n) =
5 months
15 months
​
=3 periods

Rate per 5 months (R
′
) = 12%×
12
5
​
=5% per period

Using the formula for the amount:

A
2
​
=10000×(1+
100
5
​
)
3
=10000×(1.05)
3

We know (1.05)
3
=1.157625.

A
2
​
=10000×1.157625=11576.25
CI
2
​
=11576.25−10000=₹1,576.25

Difference between the two interests:

Difference=CI
2
​
−CI
1
​
=1576.25−1536=40.25
Rounding to the nearest rupee gives ₹40.