Understanding Compound Interest
Compound interest is the interest calculated on the initial principal and also on the accumulated interest from previous periods. In this case, we will calculate the compound interest on rupees 8000 for 9 months at an annual interest rate of 20%, compounded quarterly.
Given Data
- Principal (P): 8000 rupees
- Rate of Interest (R): 20% per annum
- Time (T): 9 months (which is 9/12 = 0.75 years)
- Compounding Frequency (n): Quarterly (4 times a year)
Calculating Compound Interest
1. Convert the Rate of Interest to Quarterly:
- Quarterly Rate = 20% / 4 = 5% = 0.05 (as a decimal)
2. Calculate the Number of Compounding Periods:
- Total Compounding Periods (nT) = 4 (quarters) × 0.75 (years) = 3
3. Use the Compound Interest Formula:
- The formula for compound interest is:
A = P(1 + r/n)^(nt)
- Here, A is the amount after time T.
4. Substituting the Values:
- A = 8000 * (1 + 0.05)^3
- A = 8000 * (1.157625)
- A ≈ 9261
5. Calculate Compound Interest (CI):
- CI = A - P
- CI = 9261 - 8000
- CI ≈ 1261 rupees
Conclusion
The compound interest on rupees 8000 for 9 months at an annual rate of 20%, compounded quarterly, is approximately 1261 rupees. This calculation demonstrates how interest can grow significantly over a short period when compounded frequently.