Understanding Compound Interest in Financial Mathematics

Compound interest is a fundamental concept in financial mathematics that accurately reflects the growth of an initial investment over time. This concept is not only crucial for understanding savings, loans, and investments but is also effectively illustrated through algebraic problems. One such problem involves dividing Rs 4100 into two parts with different compounding periods to achieve equal amounts.

The Problem

The task at hand is to divide Rs 4100 into two parts such that their compound amounts are equal after 2 and 3 years. The first part will be compounded annually for 2 years, and the second part will be compounded annually for 3 years. Let's break down the steps to solve this problem.

Setting Up the Equation

Suppose the first (2-year) part is Rs 410, and the second (3-year) part is Rs 4100 - 410 Rs 3690. We need to find the values such that the compound amounts are equal after 2 and 3 years.

Compound Amount Formula:
For the first part, the compound amount after 2 years is given by:

Compound Amount for the second part (3-year amount):

Equating the two compound amounts:

Dividing both sides by 410 and (1.05)^2, we get:

Working Out the Value of x

Remember, in the original problem, the second part is denoted as 4100(1 - x), where x is the proportion of the total amount. Let's denote 4100(1 - x) as the 2-year part and 410 as the 3-year part. Using the same compound interest formula, we equate the amounts:

Cancelling out 4100 from both sides:

Dividing both sides by (1.05)^2:

Rearranging the equation:

This means 47.62% of Rs 4100 is used for the 3-year compounding, and the remaining 52.38% is used for the 2-year compounding.

Conclusion

The problem of dividing Rs 4100 between two compounding periods to achieve equal amounts is a practical application of algebra and compound interest. By using the appropriate compound interest formula and solving the resulting equation, we can accurately determine the proportions of the initial amount to be allocated to each compounding period. This method can be applied to a variety of financial planning scenarios, ensuring optimal growth over different time horizons.

Further Reading and Resources

For more information on compound interest, algebraic problem solving, and financial mathematics, refer to the following resources:

Wikipedia: Compound Interest Math Is Fun: Compound Interest Investopedia: Compound Interest

Understanding these concepts can help individuals make informed decisions in personal and corporate finance.