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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% perannum 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 1/2year 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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Half Yearly Compound [00:05:17]
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