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Rate Compounded Annually Or Half Yearly (Semi Annually)

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The time period after which the interest is added each time to form a new principal is called the conversion period. When the interest is compounded half yearly, there are two conversion periods in a year each after 6 months. In such situations, the half yearly rate will be half of the annual rate. 
In this case, there are 4 conversion periods in a year and the quarterly rate will be one-fourth of the annual rate.
 Let us see what happens to Rs. 100 over a period of one year if an interest is compounded annually or half yearly.

P = ₹ 100 at 10% per
annum compounded annually
P = ₹100 at 10% per annum  compounded half yearly
The time period taken is 1 year    The time period is 6 months or `1/2`year
I = `₹ (100 xx 10 xx 1)/100` = Rs. 10 `I = ₹ (100 xx 10 xx 1/2)/100` = ₹ 5
A = ₹100 + ₹10
= ₹ 110
A = ₹ 100 + ₹ 5 = ₹ 105 
Now for next 6 months the P = ₹105
 

So, `I = ₹ (105 xx 10 xx 1/2)/100` = ₹ 5.25

and    A = ₹ 105 + ₹ 5.25 = ₹ 110.25

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