**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 1^{st}year, P

_{1}= Rs 10,000

∴Principle for the 2

^{nd}year, P_{2}= Rs 10,000 + Rs 800 = Rs 10800∴Amount at the end of 2

^{nd}year, A = Rs 10,800 + Rs 864 = Rs 11664Interest (compound interest) that can be earned at the end of 2

^{nd}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 4

^{th}half year (i.e., at the end of 2 years), A = Rs 11248.64 + Rs 449.9456 = Rs 11698.5856 ≈ Rs 11698.59Interest (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!

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