Understanding Compound Interest: Calculating the Amount to be Paid Back at the End of 2 Years

Compound interest is a financial concept that can significantly impact the amount of money you need to repay, especially over extended periods. In this article, we'll explore a practical example of calculating the amount to be paid back over a two-year period, utilizing the provided parameters. We'll also discuss the differences between compound and simple interest.

Problem Statement

A sum of Rs. 5000 is borrowed at a rate of 12 per annum, compounded annually for a period of 2 years. The objective is to determine the total amount to be paid back at the end of the 2-year period.

Compounding Interest Calculation

The formula for calculating the amount for compound interest is:

A P(1 r/100)^T

P Principal amount (Rs. 5000) r Rate of interest (12%) T Time period (2 years)

Substituting these values into the formula:

A 5000 left(1 frac{12}{100}right)^2

This simplifies to:

A 5000 × (1.12)^2

Calculating the above:

A 5000 × 1.2544 Rs. 6272

Breakdown of the Calculation

Let's break down the steps of the calculation in a more detailed manner:

A  5000 (1   12/100)^2A  5000 (1   0.12)^2A  5000 (1.12)^2A  5000 × 1.2544A  6272

Therefore, the total amount to be paid back at the end of 2 years, considering compound interest, is Rs. 6272.

Monthly Compounding Interest Calculation

For more frequent compounding, such as monthly, the formula is slightly different. The formula for monthly compounding is:

A P (1 r/100/m)^(mT)

Where:

m Number of times interest is compounded per year (12 for monthly compounding)

Substituting the values:

A 5000 (1 12/100/12)^(12×2)

This simplifies to:

A 5000 (1 0.01)^24

Calculating the above:

A 5000 × 1.01^24

Using a calculator:

A 5000 × 1.26973 Rs. 6348.65

Therefore, the total amount to be paid back at the end of 2 years, considering monthly compounding, is approximately Rs. 5635.80.

Comparison with Simple Interest

For the same period, if the interest were calculated using simple interest instead, the calculation would be:

A P PRT/100

Substituting the values:

A 5000 5000 × .06 × 2

This simplifies to:

A 5000 600 Rs. 5600

Conclusion

Compound interest results in a higher amount to be paid back over time compared to simple interest. The formula and frequency of compounding are crucial in calculating the total amount. Understanding these calculations can help individuals make informed financial decisions.

Related Keywords

Compound interest Repayment amount Rate of interest

References

If you need further detailed information or want to explore the details of compound interest and its applications, visit relevant financial and educational resources.