Understanding Compound Interest
When you invest money, you can earn interest on it. Compound interest means that the interest you earn is added to your principal, and you earn interest on that new total in subsequent periods.
Details of the Investment
- Principal Amount (P): Rs. 10,000
- Rate of Interest (R): 8% per annum
- Time (T): 1 year
- Compounding Frequency: Half-yearly (every 6 months)
Calculating the Compound Interest
To calculate compound interest that is compounded half-yearly, we need to determine the number of compounding periods and the interest rate per period.
- Number of Compounding Periods (n): Since it's compounded half-yearly for 1 year, there are 2 periods (6 months each).
- Interest Rate per Period (r):
- Annual Rate: 8%
- Half-Yearly Rate: 8% / 2 = 4%
Formula for Compound Amount
The formula to calculate the compound amount is:
- A = P (1 + r/n)^(nt)
Where:
- A = Total amount after time T
- P = Principal amount
- r = Annual interest rate (as a decimal)
- n = Number of times interest is compounded per year
- t = Number of years
Plugging in the Values
- A = 10000 * (1 + 0.04)^2
- A = 10000 * (1.04)^2
- A = 10000 * 1.0816
- A = Rs. 10,816
Total Amount and Interest Earned
- Total Amount (A): Rs. 10,816
- Compound Interest Earned:
- CI = A - P = 10,816 - 10,000 = Rs. 816
Conclusion
After 1 year, with Rs. 10,000 invested at an 8% annual interest rate compounded half-yearly, you will have a total of Rs. 10,816, earning Rs. 816 in compound interest.