Introduction

Calculating interest accrued over a specific period using a given principal amount and annual interest rate is a common task in financial planning. This article provides a detailed step-by-step explanation of how to calculate the interest on Rs 600 over a period that spans 3 years, 6 months, and 20 days, at an annual interest rate of 6%. Understanding and applying this calculation can be crucial for personal finance management, investment decisions, and business operations. This guide will walk you through the process, including relevant formulas and examples.

Understanding the Problem

The principal amount, denoted as ( P ), is Rs 600. The annual interest rate, denoted as ( r ), is 6%. The time period, ( t ), needs to be converted into years for the calculation. Here, the period is 3 years, 6 months, and 20 days. We will convert this period into years for the calculation. The interest, ( I ), is calculated using either simple interest or compound interest depending on the circumstances.

Simple Interest Calculation

Simple interest is calculated using the formula:

[ I P times r times t ]

In this scenario, the simple interest calculation would be:

[ I 600 times frac{6}{100} times 3.561 ]

Where 3.561 years is the total time period (3 years 6 months 20 days 3 0.5 (frac{20}{365}) ≈ 3.561 years).

Now, let's perform the calculation:

[ I 600 times 0.06 times 3.561 approx 126 ]

Therefore, the interest accrued over the period is approximately Rs 126.

Compound Interest Calculation

Compound interest, on the other hand, is calculated using the formula:

[ A P left(1 frac{r}{n}right)^{nt} ]

Where ( A ) is the amount after interest, ( n ) is the number of times interest is compounded per year, and ( t ) is the time the money is invested or borrowed for, in years. If interest is compounded annually, ( n 1 ).

For Rs 600 at 6% compounded annually for 3 years, 6 months, and 20 days, the calculation would be:

[ A 600 left(1 frac{0.06}{1}right)^{1 times 3.561} approx 600 times (1.06)^{3.561} approx 600 times 1.247 approx 748.20 ]

The interest earned would be:

[ I A - P approx 748.20 - 600 approx 148.20 ]

Thus, the compound interest accrued over the same period is approximately Rs 148.20.

Conclusion

The calculations show that the simple interest on Rs 600 over 3 years, 6 months, and 20 days at 6% annual interest rate is approximately Rs 126, while the compound interest is approximately Rs 148.20. Understanding these concepts is vital for making informed financial decisions. Whether you are calculating interest for a savings account, loans, or investments, these calculations can provide valuable insights.

Key Takeaways:

Interest Calculation: Understanding the difference between simple and compound interest is essential for accurate financial planning. Convert Periods: Always convert the time period into years for accurate calculations. Apply Different Rates: Simple interest is less complex, while compound interest yields more significant returns, especially over longer periods or higher rates.

Related Topics:

Simple Interest Calculation: How to calculate interest without compounding. Annual Interest Rate: Techniques for calculating interest based on annual rates. Compound Interest: Handles compounding periods for a more accurate long-term interest calculation.