#### notes

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 |