Find the principal that will amount to N1200 at \( 5 \% \) per annum for 3 years, to the nearest whole number \( \begin{array}{lll}\text { (a) } 22560 & \text { (b) N3050 } \\ \text { (c) N1043 } & \text { (d) } \$ 5000\end{array} \)

To find the principal (P), we can use the formula for compound interest: \[ A = P(1 + r)^n \] Where: - \( A \) is the amount after time \( n \) - \( r \) is the rate of interest (as a decimal) - \( n \) is the number of years In this case, \( A = N1200 \), \( r = \frac{5}{100} = 0.05 \), and \( n = 3 \). Rearranging the formula to solve for \( P \): \[ P = \frac{A}{(1 + r)^n} \] Substituting the values: \[ P = \frac{1200}{(1 + 0.05)^3} \] \[ P = \frac{1200}{(1.157625)} \] \[ P \approx 1036.19 \] Rounding to the nearest whole number gives us \( N1036 \). Now, comparing with the options, the closest option is: (c) N1043. --- The concept of calculating the principal using interest formulas has practical implications in various real-life scenarios like loans, savings accounts, or investments. Knowing how much you need to invest now to achieve a certain amount in the future can help with budgeting and financial planning, making your money work more effectively for you! Additionally, when dealing with interest calculations, be careful with the interest type: compound vs. simple interest. Each has its own formula and application. Compound interest can grow your money faster, as it earns interest on both the principal and the accumulated interest from previous periods—this is sometimes referred to as "earning interest on interest."