Introduction:
Compound interest is the interest that is calculated on both the principal amount and the interest accumulated on it. The frequency at which the interest is compounded affects the final amount that is earned.

Given:
Principal amount (P) = Rs. 10000
Time (t) = 18 months
Rate of interest (r) = 10% per annum

Calculation:
Firstly, we need to calculate the interest that would be earned if the interest is compounded yearly.

Yearly Compounding:
The formula for calculating the compound interest when compounded yearly is:

A = P(1 + r/n)^(n*t)

Where,
A = final amount
P = principal amount
r = rate of interest
n = the number of times the interest is compounded in a year
t = time period in years

Here, n = 1 (as the interest is compounded yearly)

A = 10000(1 + 0.1/1)^(1*1.5) = Rs. 11610.51

The interest earned would be Rs. 1610.51

Half-Yearly Compounding:
The formula for calculating the compound interest when compounded half-yearly is:

A = P(1 + r/n)^(n*t)

Where,
A = final amount
P = principal amount
r = rate of interest
n = the number of times the interest is compounded in a year
t = time period in years

Here, n = 2 (as the interest is compounded half-yearly)

A = 10000(1 + 0.1/2)^(2*1.5) = Rs. 11636.08

The interest earned would be Rs. 1636.08

Difference:
The difference between the interest earned when compounded yearly and half-yearly is:

1636.08 - 1610.51 = Rs. 25.57

Therefore, the difference between the compound interest compounded yearly and half-yearly on Rs. 10000 for 18 months at 10% per annum is Rs. 25.57.

Find the difference between the compound interest compounded yearly and half-yearly on Rs. 10000 for 18 months at 10% per annum. Then, find the amount for the compound interest compounded half yearly by applying the formula A=P(1+r2x100}t×2. Then subtract the principal from the amount to get the interest.