Determine the minimum amount of money they would have to invest which would have accrued to R280 000.

Here are the solutions to your questions: 5.2.1 Step 1: Determine the effective annual interest rate for Bank A. Bank A offers an effective interest rate of 12% per annum. i_A = 0.12 Step 2: Determine the effective annual interest rate for Bank B. Bank B offers an interest rate of 11.5% p.a., compounded monthly. The formula for the effective annual interest rate is i_eff = (1 + i_nomm)^m - 1, where i_nom is the nominal interest rate and m is the number of compounding periods per year. i_B = (1 + (0.115)/(12))^12 - 1 i_B = (1 + 0.0095833333)^12 - 1 i_B ≈ (1.0095833333)^12 - 1 i_B ≈ 1.12130508 - 1 i_B ≈ 0.12130508 Step 3: Compare the effective annual interest rates. Bank A: 12\% Bank B: 12.130508\% Since 12.130508\% > 12\%, Bank B offers the better interest rate. The bank that offers the best interest rate is Bank B. 5.2.2 Step 1: Identify the effective annual interest rate to be used. From 5.2.1, Bank B offers the best interest rate, which is i = 0.12130508. Step 2: Set up the equation for the initial investment. Let P be the initial investment. The investment needs to accrue to R280 000 in 5 years. A withdrawal of R50 000 is made after 2 years. The formula for the initial investment (P) when there is an intermediate withdrawal (W) is: P = (FV)/((1+i)^n) + (W)/((1+i)^k) where FV is the final future value, n is the total number of years, W is the withdrawal amount, and k is the number of years until the withdrawal. Given: FV = R280000 n = 5 years W = R50000 k = 2 years i = 0.12130508 Step 3: Substitute the values into the formula and calculate. P = (280000)/((1+0.12130508)^5) + (50000)/((1+0.12130508)^2) P = (280000)/((1.12130508)^5) + (50000)/((1.12130508)^2) P ≈ (280000)/(1.772590) + (50000)/(1.257290) P ≈ 157960.67 + 39768.68 P ≈ 197729.35 Step 4: Round the answer to the nearest rand. The minimum amount of money they would have to invest is R197729. That's 2 down. 3 left today — send the next one.