Compound Interest for 3rd Year

This solution calculates the specific interest earned only during the third year of an investment, using the compound interest method.

Key Financial Details

• Principal Amount (P): 74,000 rupees
• Annual Interest Rate (R): 12%
• Compounding Period: Annually

Amount Calculation After 2 Years

First, determine the total amount accumulated after the first two years. The formula for the future value (Amount, A) with compound interest is $A = P(1 + \frac{R}{100})^n$, where n is the number of years.

• Using the formula for n=2 years:
• $A_2 = 74000 \times (1 + \frac{12}{100})^2$
• $A_2 = 74000 \times (1.12)^2$
• $A_2 = 74000 \times 1.2544$
• $A_2 = 92,825.60$ rupees

Amount Calculation After 3 Years

Next, calculate the total amount accumulated after three full years using the same compound interest formula.

• Using the formula for n=3 years:
• $A_3 = 74000 \times (1 + \frac{12}{100})^3$
• $A_3 = 74000 \times (1.12)^3$
• $A_3 = 74000 \times 1.404928$
• $A_3 = 103,964.672$ rupees

Determining 3rd Year Interest

The interest earned specifically during the third year is the difference between the total amount at the end of year 3 ($A_3$) and the total amount at the end of year 2 ($A_2$).

• Interest (3rd Year) = $A_3 - A_2$
• Interest (3rd Year) = $103,964.672 - 92,825.60$
• Interest (3rd Year) = $11,139.072$ rupees

Therefore, the interest for the 3rd year, rounded to two decimal places, is 11,139.07 rupees.