To find the principal amount that will amount to N5,500 at a simple interest rate of 2% per annum over 5 years, we can use the formula for simple interest. Let's break this down step-by-step. ### Step 1: Understand the Simple Interest Formula The formula for calculating the total amount (A) in simple interest is: \[ A = P + I \] Where: - \( A \) is the total amount after interest. - \( P \) is the principal amount (the initial amount of money). - \( I \) is the interest earned. The interest \( I \) can be calculated using the formula: \[ I = P \times r \times t \] Where: - \( r \) is the rate of interest (as a decimal). - \( t \) is the time in years. ### Step 2: Rearranging the Formula Since we need to find the principal \( P \), we can rearrange the total amount formula: \[ A = P + I \implies I = A - P \] Substituting the interest formula into this gives: \[ A = P + (P \times r \times t) \] This can be simplified to: \[ A = P(1 + rt) \] ### Step 3: Plugging in the Values Now, we know: - \( A = N5,500 \) - \( r = 2\% = 0.02 \) - \( t = 5 \) years Substituting these values into the equation: \[ 5,500 = P(1 + 0.02 \times 5) \] Calculating \( 0.02 \times 5 \): \[ 0.02 \times 5 = 0.1 \] So, we have: \[ 5,500 = P(1 + 0.1) = P(1.1) \] ### Step 4: Solving for Principal \( P \) Now, we can solve for \( P \): \[ P = \frac{5,500}{1.1} \] Calculating this gives: \[ P = 5,000 \] ### Conclusion Thus, the principal amount that will amount to N5,500 at a simple interest rate of 2% per annum over 5 years is **N5,000**. ### Explanation of Options - **Option A: N4,900** - This is incorrect because it does not satisfy the simple interest formula when calculated with the given rate and time. - **Option B: N5,000** - This is the correct answer as shown in our calculations. - **Option C: N4,700** - This is also incorrect for the same reasons as above; it does not yield the correct total amount. - **Option D: N4,800** - This option is incorrect as well; it does not satisfy the conditions of the problem. ### Revision Summary - The formula for total amount in simple interest is \( A = P(1 + rt) \). - Rearranging gives \( P = \frac{A}{1 + rt} \). - Substitute the values for \( A \), \( r \), and \( t \) to find \( P \). - The correct principal amount is N5,000, which is option B.