Question

A sum of ₹2,00,000 is invested for 2 years at an annual interest rate of \(20\%\)per annum compounded half yearly. After 2 years, the amount is invested again at \(30\%\)simple interest per annum for 1 year. What will be the final amount after 3 years?

• A. Rs.3,61,808
• B. Rs.3,80,666
• C. Rs.2,92,820
• D. Rs.3,28,914

Answer 1

The Correct Option is B

Compound and Simple Interest Calculation 

- The principal amount is Rs. 2,00,000, and the interest rate is 20% per annum compounded half yearly for the first 2 years.

Step 1: Compound Interest Calculation for the First 2 Years

The formula for compound interest is:

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

Where:

• \( P = 2,00,000 \) (Principal)
• \( r = 20\% = 0.2 \) (Annual interest rate)
• \( n = 2 \) (Number of times interest is compounded per year)
• \( t = 2 \) years

Substituting the values:

\[ A = 2,00,000 \left( 1 + \frac{0.2}{2} \right)^{2 \times 2} \] \[ = 2,00,000 \left( 1 + 0.1 \right)^4 \] \[ = 2,00,000 \times (1.1)^4 = 2,00,000 \times 1.4641 = 2,92,820 \]

After 2 years, the amount becomes Rs. 2,92,820.

Step 2: Simple Interest Calculation for the Next 1 Year

The formula for simple interest is:

\[ A = P \left( 1 + r \times t \right) \]

Where:

• \( P = 2,92,820 \)
• \( r = 30\% = 0.3 \)
• \( t = 1 \) year

Substituting the values:

\[ A = 2,92,820 \times (1 + 0.3) \] \[ = 2,92,820 \times 1.3 = 3,80,666 \]

Conclusion: The final amount after 3 years is Rs. 3,80,666.