Understanding Compound Interest: A Detailed Example with Rs. 222,500

Compound interest can be a powerful tool for growing your wealth over time. This article will walk you through a detailed example of calculating the compound interest for a principal amount of Rs. 222,500 over a period of 2 years at a rate of 49 percent per annum. We will cover the calculations using both the exponential and simple multiplicative methods.

Exponential Compound Interest Formula

The exponential formula for compound interest is given by:

A P times; ertimes;t

A Amount P Principal amount (Rs. 222,500 in our example) r Rate of interest in decimal form (0.49) t Time period in years (2 years) e Natural base of logarithm (approximately equal to 2.71828)

Calculating Using the Exponential Formula

Let's plug in the numbers:

A 222,500 times; e0.49 times; 2

A 222,500 times; e0.98

Using e ^ 0.98 ≈ 2.6644562419, we can find:

A 222,500 times; 2.6644562419 ≈ 592,842

Calculating Compound Interest

Compound interest can be calculated using the formula:

Compound Interest A - P

Compound Interest 592,842 - 222,500 370,342

Annual Compounding Formula

Assuming the interest is compounded annually, we use the formula:

A P times; (1 r / 100)n

P Principal amount (Rs. 222,500) r Rate of interest in percent (49%) n Number of years (2 years)

Calculating Using the Annual Compounding Formula

Let's use the provided values:

A 222,500 times; (1 0.49)2

A 222,500 times; 1.492

A 222,500 times; 2.2201 ≈ 493,972.25

Calculating Compound Interest with Annual Compounding

The compound interest is calculated as:

Compound Interest 493,972.25 - 222,500 271,472.25

Both methods have provided different values due to the nature of the exponential and multiplicative compounding formulas. The exponential formula gives a slightly different result due to the use of the natural base e, while the multiplicative method gives a more straightforward result based on the given interest rate.

Conclusion

Understanding how to calculate compound interest using different methods can be crucial for financial planning and investment. Whether you use the exponential formula or the annual compounding method, it is essential to choose the method that best suits your needs and the specifics of your financial situation.

Keywords: compound interest, interest calculation, annual compounding