Choose the correct alternative Ramesh borrowed an amount of Rs. 75000 from one of his friends at a compound interest of \( 2 \% \) p.a., which gets compunded half yearly. Find the approximate amount returned by Ramesh at the end of 2 years?

To calculate the amount returned by Ramesh at the end of 2 years when he borrowed Rs. 75,000 at a compound interest rate of 2% per annum compounded half yearly, we can use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) = the amount of money accumulated after n years, including interest. - \( P \) = the principal amount (Rs. 75,000). - \( r \) = annual interest rate (decimal) = 2% = 0.02. - \( n \) = number of times that interest is compounded per year = 2 (half yearly). - \( t \) = the number of years the money is borrowed = 2. Now let's plug in the values: \[ A = 75000 \left(1 + \frac{0.02}{2}\right)^{2 \times 2} \] \[ A = 75000 \left(1 + 0.01\right)^{4} \] \[ A = 75000 \left(1.01\right)^{4} \] Calculating \( (1.01)^4 \): \[ (1.01)^4 \approx 1.04060401 \] So, now substitute back into the equation: \[ A \approx 75000 \times 1.04060401 \approx 78045.30 \] Thus, the approximate amount returned by Ramesh at the end of 2 years is around Rs. 78,045.