Rate Compounded Annually or Half yearly

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 2 conversion period in a year each after 6 months. In such situations, the half yearly rate will be half of the annual rate. For interest is compounded quartely, there are 4 conversion periods in a year and the quartely rate will be one-fourth of the animal rate.

Let us consider Rs. 200 over a period of one year if an interest is compounded annually on half yearly.

 P = Rs. 200 at 10% per annum compounded annually P = Rs. 200 at 10% per annum compounded half-yearly The time period taken is 1 year The time period is 6 months or year A = Rs. 200 + Rs. 20 = Rs. 220 A = Rs. 200 + Rs. 10 = Rs. 210 For next 6 month P = Rs. 210

Examples

What amount is to be repaid on a loan of Rs. 15000 for years at 10% per annum compounded half yearly.

Solution

There are 3 half years in years.

Compounding has to be done in 3 times.

Rate of interest = half of 10% = 5% half yearly.

Example

Find CI paid when a sum of Rs. 50,000 invested for 1 year and 3 months at per annum compounded annually.

Solution

To convert the time in year

1 year 3 months

To find the amount, first we have to find the amount for whole part i.e., 1 year in this case. Then use this as principal to get simple interest foryear more.

Find SI on Rs. 54250 foryear.

Interest for first year = Rs. 54250 - Rs. 50000 = Rs. 4250.

Interestyear = 1152.81

Total compound Interest = 4250 + 1152.81 = Rs. 5402.81