WHAT DO U MEAN BY : RATE COMPOUNDED ANNUALLY OR HALF YEARLY ( SEMI ANNUALLY)
Hi Anuj!
Rate is compounded annually means that the interest is calculated for each year.
Suppose Rs 10,000 is borrowed by Ram for 2 years at the rate of 8% per annum compound annually.
Here, principle for the 1st year, P1 = Rs 10,000.png)
∴Principle for the 2nd year, P2 = Rs 10,000 + Rs 800 = Rs 10800
.png)
∴Amount at the end of 2nd year, A = Rs 10,800 + Rs 864 = Rs 11664
Interest (compound interest) that can be earned at the end of 2nd year = Rs (11664 – 10000) = Rs 1664.
Note: Rs 800 + Rs 864 = Rs 1664
Rate is compounded half yearly means that the interest is calculated for each half year (i.e. for six months).
Suppose Rs 10,000 is borrowed by Ram for 2 years at the rate of 8% per annum compounded half yearly.
Here, principle for the first six months = Rs 10,000. Rate, R = 8% per annum = 4% per half year 
∴Amount at the end of 4th half year (i.e., at the end of 2 years), A = Rs 11248.64 + Rs 449.9456 = Rs 11698.5856 ≈ Rs 11698.59
Interest (compound interest) that can be earned at the end of 2 years = Rs (11698.59 – 10000) = Rs 1698.59.
Note: Rs 400 + Rs 416 + Rs 432.64 + Rs 449.9456 = RS 1698.5856 ≈ Rs 1698.59
Rate is compounded quarterly means that the interest is calculated for each quarter (i.e. for 3 months).
In this, compound interest and amount for the same problem when the interest is compounded quarterly can be calculated.
Hope! You got the meaning.
Cheers!