Calculating Compound Interest for Rs 12,000 at 20% Per Annum Compounded Half-Yearly
Understanding compound interest is crucial for managing personal finances and planning for future financial goals. This article will explain how to calculate the compound interest for a principal amount of Rs 12,000 over a period of 2 years at an annual interest rate of 20%, compounded half-yearly. We'll also explore the formula and provide a detailed solution to this financial calculation problem.
Understanding Compound Interest
Compound interest is a financial concept where interest is added to the principal amount, and the accumulated interest is then also added to subsequent calculations of interest. This means that interest is earned not only on the principal but also on the interest that has been earned previously. This is a powerful concept in personal and business finance, as it can significantly increase the growth of an investment over time.
Formula for Compound Interest
The formula for calculating compound interest is:
A P (1 r/n) ^ (nt)
Where:
A is the amount of money accumulated after n periods, including interest. P is the principal amount (initial investment). r is the annual interest rate (decimal). n is the number of times that interest is compounded per year. t is the time the money is invested for, in years.For this specific problem, the principal amount (P) is Rs 12,000, the annual interest rate (r) is 20% or 0.20, the interest is compounded half-yearly (n 2), and the time period (t) is 2 years.
Step-by-Step Calculation
Step 1: Convert the annual interest rate to a half-yearly interest rate.
The annual interest rate is 20%, so the half-yearly interest rate is 10% or 0.10.
Step 2: Calculate the number of times interest is compounded.
Since the interest is compounded half-yearly, in 2 years (t 2), the interest is compounded 4 times (n 4).
Step 3: Apply the compound interest formula.
A 12000 (1 0.10/2) ^ (2*2)
A 12000 (1 0.05) ^ 4
A 12000 (1.05) ^ 4
A 12000 * 1.21550625
A 14586.075
Therefore, the amount accumulated after 2 years is Rs 14,586.08.
Calculating Compound Interest
The compound interest (CI) can be calculated by subtracting the principal amount (P) from the accumulated amount (A).
CI A - P
CI 14586.075 - 12000
CI Rs 2586.075
Thus, the compound interest for Rs 12,000 at 20% per annum compounded half-yearly over 2 years is Rs 2,586.075.
Common Mistakes to Avoid
One common mistake in calculations is forgetting to convert the annual interest rate into a half-yearly rate before applying it in the formula. Another mistake is mishandling the number of compounding periods (n) during the calculation.
Conclusion
Understanding the steps involved in calculating compound interest and using the appropriate formula can greatly aid in personal financial planning. In the case of Rs 12,000 at 20% per annum compounded half-yearly over 2 years, the compound interest is Rs 2,586.075. This knowledge can help individuals and businesses make informed financial decisions and plan for the future.