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
What amount is to be repaid on a loan of Rs. 15000 for years at 10% per annum compounded half yearly.
There are 3 half years in years.
Compounding has to be done in 3 times.
Rate of interest = half of 10% = 5% half yearly.
Find CI paid when a sum of Rs. 50,000 invested for 1 year and 3 months at per annum compounded annually.
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