Understanding Compound Interest: A 12-Year Growth Calculation

Compound interest is a fundamental concept in finance, and its power can be harnessed to grow an initial sum of money over time. In this article, we will explore how a sum of Rs. 4800 grows to Rs. 6000 in 4 years, and then use this information to determine the value after 12 years. By following the compound interest formula and calculations, we will uncover the underlying rate of interest and its impact over a longer period.

Understanding the Given Problem

Given the initial principal P Rs. 4800, and the amount A after 4 years A Rs. 6000, we need to find the compound interest rate and subsequently calculate the amount after 12 years.

Step 1: Determining the Rate of Interest

The formula for compound interest is given by:

A P (1 r/100)t

Substituting the given values into this formula:

6000 4800 (1 r/100)4

Dividing both sides by 4800:

(6000/4800) (1 r/100)4

1.25 (1 r/100)4

To solve for (1 r/100), we take the fourth root of both sides:

1 r/100 1.25^(1/4)

Calculating the fourth root of 1.25:

1 r/100 1.05737

Therefore:

r/100 1.05737 - 1

r 0.05737 * 100

r 5.737

The rate of interest is approximately 5.737% per annum.

Step 2: Calculating the Amount After 12 Years

Now, using the rate of interest r 5.737%, we calculate the amount after 12 years:

A P (1 r/100)^(12)

Substituting the values:

A 4800 (1 5.737/100)^12

A 4800 (1.05737)^12

Calculating (1.05737)^12:

(1.05737)^12 ≈ 1.791

Substituting back:

A ≈ 4800 * 1.791 ≈ 8596.80

Therefore, the sum after 12 years will be approximately Rs. 8596.80.

Summary

This example demonstrates the power of compound interest over a longer period. By knowing the initial sum, the final amount after a certain number of years, and the interval at which interest is compounded, we can accurately determine the interest rate and predict the future value. This knowledge is crucial for both personal and business financial planning.

Conclusion

Understanding and applying the compound interest formula is essential for anyone managing their finances or planning for long-term financial goals. Whether it's for personal savings, investments, or business growth, the growth over time can be significantly enhanced with compound interest.