Understanding Compound Interest on Rupees 10,000 at 20% per Annum for 9 Months, Compounded Quarterly
Understanding compound interest is crucial for managing personal finances and making informed financial decisions. In this article, we will explore how to calculate compound interest on Rupees 10,000 at a 20% annual rate for 9 months when the interest is compounded quarterly.
Calculation of Compound Interest
The formula for compound interest is given by:
CI P (1 R/n)^(nt) - P
Where:
P is the principal amount (Rs. 10,000 in this case) R is the annual interest rate (20%) n is the number of times interest is compounded per year (quarterly in this case, so 4) t is the time the money is invested or borrowed for, in years (9 months 0.75 years) CI is the compound interestCalculation Example
Using the formula, we can calculate the compound interest as follows:
CI 10000 (1 0.20/4)^(4 x 0.75) - 10000
Breaking it down step by step:
R/n 0.20/4 0.05 1 0.05 1.05 (1.05)^3 1.157625 CI 10000 (1.157625 - 1) 10000 x 0.157625 1576.25Hence, the compound interest on Rupees 10,000 at 20% per annum for 9 months, compounded quarterly, is Rs. 1576.25.
Alternative Method: Quarterly Repeated Addition of Interest
Alternatively, we can break down the problem into quarters and calculate the interest for each quarter:
Principal (P) 10,000 Rate of Interest (R) 20% per annum or 5% per quarter Time period (N) 9 months 3 quartersFor the first quarter:
Interest for the 1st quarter 10000 x 5/100 500
New principal 10000 500 10500
For the second quarter:
Interest for the 2nd quarter 10500 x 5/100 525
New principal 10500 525 11025
For the third quarter:
Interest for the 3rd quarter 11025 x 5/100 551.25
Total compound interest 500 525 551.25 1576.25
This confirms the earlier calculation, showing that the total compound interest on Rs. 10,000 at 20% per annum for 9 months, compounded quarterly, is Rs. 1576.25.
Conclusion
Calculating compound interest, especially when it is compounded quarterly, involves understanding the formula and breaking down the time periods. By applying the formula and breaking it down into quarters, we can accurately determine the compound interest earned on a principal amount over a given period.