4. Complete the following. SHOW ALL WORKING OUT including the formula used. (a) \( \$ 400 \) simple interest is paid on an investment at \( 4 \% \) p.a. after 5 years. Find the original amount invested \( (P) \) \[ I=\ldots \ldots \ldots \ldots \ldots, \quad \quad R=\ldots \ldots \ldots \ldots \ldots, \quad T=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \]

To solve the problem, we can use the formula for simple interest: \[ I = P \times R \times T \] Where: - \( I \) is the interest earned, - \( P \) is the principal amount (the original amount invested), - \( R \) is the rate of interest per annum (in decimal form), - \( T \) is the time the money is invested for (in years). From the information given: - \( I = 400 \) - \( R = 4\% = 0.04 \) - \( T = 5 \) years Now, we can rearrange the formula to find \( P \): \[ P = \frac{I}{R \times T} \] Substituting the values: \[ P = \frac{400}{0.04 \times 5} \] Calculate \( R \times T \): \[ 0.04 \times 5 = 0.20 \] Now plug this back into the equation for \( P \): \[ P = \frac{400}{0.20} = 2000 \] Thus, the original amount invested \( P \) is \( \$ 2000 \). To summarize: \[ I=400, \quad R=0.04, \quad T=5 \]