To solve the problem, we need to determine the interest on N250.00 for 6 months, given that the interest on N150.00 for 2.5 years is N4.50. We will follow these steps: ### Step 1: Calculate the Interest Rate First, we need to find the interest rate from the information provided. We know: - Principal (P) = N150.00 - Time (T) = 2.5 years - Interest (I) = N4.50 The formula for simple interest is: \[ I = P \times r \times T \] Where: - \( I \) is the interest earned, - \( P \) is the principal amount, - \( r \) is the rate of interest per year (in decimal), - \( T \) is the time in years. Rearranging the formula to find the rate \( r \): \[ r = \frac{I}{P \times T} \] Substituting the known values: \[ r = \frac{4.50}{150 \times 2.5} \] Calculating the denominator: \[ 150 \times 2.5 = 375 \] Now substituting back into the equation for \( r \): \[ r = \frac{4.50}{375} = 0.012 \] To express this as a percentage, we multiply by 100: \[ r = 0.012 \times 100 = 1.2\% \] ### Step 2: Calculate the Interest for N250.00 for 6 Months Now that we have the interest rate, we can calculate the interest on N250.00 for 6 months. First, we need to convert 6 months into years: \[ T = \frac{6}{12} = 0.5 \text{ years} \] Now we can use the simple interest formula again: \[ I = P \times r \times T \] Where: - \( P = N250.00 \) - \( r = 0.012 \) (from our previous calculation) - \( T = 0.5 \) Substituting these values into the formula: \[ I = 250 \times 0.012 \times 0.5 \] Calculating the interest: \[ I = 250 \times 0.012 = 3.00 \] \[ I = 3.00 \times 0.5 = 1.50 \] ### Final Answer The interest on N250.00 for 6 months at the same rate is **N1.50**. ### Explanation of Other Options - **Option B (N7.50)**: This amount is too high for the interest calculated based on the rate we derived. It does not align with the calculations we performed. - **Option C (N15.00)**: This amount is also too high. It would imply a much higher interest rate or a longer time period than what we have. - **Option D (N18.00)**: This is significantly higher than what we calculated. It suggests an unrealistic interest accumulation for the given principal and time. ### Revision Summary - The interest rate was calculated from the initial conditions using the simple interest formula. - The interest on N250.00 for 6 months was calculated using the same interest rate. - The correct answer is N1.50, as derived from the calculations. - Always ensure to convert time into years when using the simple interest formula.