Compound Interest Calculation for ₹4500

Given Information

• Principal Amount (P): ₹4500
• Annual Interest Rate (R): 12%
• Time Period (T): 2 years and 8 months
• Compounding Frequency: Annually

Formula for Annual Compounding with Fractional Year

To calculate the total amount (A) when interest is compounded annually but the time period includes a fraction of a year, we use the following approach:

A = P \times (1 + \frac{R}{100})^n \times (1 + \frac{R}{100} \times \frac{t}{k})

Where:

• P = Principal Amount
• R = Annual Interest Rate
• n = Number of complete years
• t = Number of months in the fractional part of the year
• k = 12 (number of months in a year)

Calculation Steps

1. Convert the time period:

   The time period is 2 years and 8 months. The fractional part is 8 months.

   Fractional year = \frac{8 \text{ months}}{12 \text{ months}} = \frac{2}{3} \text{ years}

2. Calculate amount after full years:

   Calculate the amount accumulated after the 2 full years using the standard compound interest formula for the whole years.

   Amount after 2 years = P \times (1 + \frac{R}{100})^n

   Amount after 2 years = 4500 \times (1 + \frac{12}{100})^2

   Amount after 2 years = 4500 \times (1.12)^2

   Amount after 2 years = 4500 \times 1.2544

   Amount after 2 years = ₹5644.80

3. Calculate interest for the fractional year:

   Calculate simple interest on the amount obtained after 2 years for the remaining 8 months (2/3 of a year).

   Interest for 8 months = Amount after 2 years \times \frac{R}{100} \times \frac{t}{k}

   Interest for 8 months = 5644.80 \times \frac{12}{100} \times \frac{8}{12}

   Interest for 8 months = 5644.80 \times 0.12 \times \frac{2}{3}

   Interest for 8 months = 5644.80 \times 0.08

   Interest for 8 months = ₹451.584

4. Calculate the total amount:

   Add the interest for the fractional period to the amount after the complete years.

   Total Amount (A) = Amount after 2 years + Interest for 8 months

   Total Amount (A) = 5644.80 + 451.584

   Total Amount (A) = ₹6096.384

Final Amount

The total amount accumulated after 2 years and 8 months, rounded to two decimal places, is ₹6096.38.