- **Calculation of Interest on the Principal Amount**
Given:
Principal amount (P) = $10,000
Rate of interest (R) = 8%
Time period (T) = 1 year
Number of times interest is compounded per year (n) = 2 (half yearly)
- **Formula for Compound Interest**
The formula to calculate compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount
r = Rate of interest
n = Number of times interest is compounded per year
t = Time period in years
- **Calculation of Compound Interest**
Substitute the given values into the formula:
A = $10,000(1 + 0.08/2)^(2*1)
A = $10,000(1 + 0.04)^2
A = $10,000(1.04)^2
A = $10,000(1.0816)
A = $10,816
- **Calculation of Compound Interest**
To find the compound interest, subtract the principal amount from the final amount:
Compound Interest = $10,816 - $10,000
Compound Interest = $816
- **Conclusion**
Therefore, the compound interest earned on $10,000 for 1 year at 8% per annum compounded half yearly is $816.