2. Find the amount and the compound interest on \( \mathrm{N} 1,00,000 \) compounded quarterly for 9 months at the rate of \( 4 \% \) per annum.

To calculate the compound interest on \( \mathrm{N} 1,00,000 \) compounded quarterly for 9 months at a 4% annual interest rate, we first need to determine the effective interest rate per quarter. The quarterly rate is \( \frac{4\%}{4} = 1\% \) per quarter. Since we are compounding for 9 months, this is equivalent to 3 quarters. The formula for compound interest is given by: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount after time \( t \), - \( P \) is the principal amount (\( \mathrm{N} 1,00,000 \)), - \( r \) is the annual interest rate (0.04), - \( n \) is the number of times interest is compounded per year (4), - \( t \) is the time in years (0.75 for 9 months). Substituting the values: \[ A = 1,00,000 \left(1 + \frac{0.04}{4}\right)^{4 \times 0.75} \] \[ A = 1,00,000 \left(1 + 0.01\right)^{3} \] \[ A = 1,00,000 \left(1.01\right)^{3} \] \[ A = 1,00,000 \times 1.030301 \approx 1,03,030.10 \] The amount \( A \) after 9 months is approximately \( \mathrm{N} 1,03,030.10 \). To find the compound interest \( CI \), subtract the principal \( P \): \[ CI = A - P = 1,03,030.10 - 1,00,000 = 3,030.10 \] So, the compound interest earned is approximately \( \mathrm{N} 3,030.10 \).