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 $i_{eff} = \left(1 + \frac{i_{nom}}{m}\right)^m - 1$, where $i_{nom}$ is the nominal interest rate and $m$ is the number of compounding periods per year. $i_B = \left(1 + \frac{0.115}{12}\right)^{12} - 1$ $i_B = (1 + 0.0095833333)^{12} - 1$ $i_B \approx (1.0095833333)^{12} - 1$ $i_B \approx 1.12130508 - 1$ $i_B \approx 0.12130508$

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 $\boxed{Bank B}$.

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: $P = \frac{FV}{(1+i)^n} + \frac{W}{(1+i)^k}$ 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. $P = \frac{280000}{(1+0.12130508)^5} + \frac{50000}{(1+0.12130508)^2}$ $P = \frac{280000}{(1.12130508)^5} + \frac{50000}{(1.12130508)^2}$ $P \approx \frac{280000}{1.772590} + \frac{50000}{1.257290}$ $P \approx 157960.67 + 39768.68$ $P \approx 197729.35$

Step 4: Round the answer to the nearest rand. The minimum amount of money they would have to invest is $\boxed{R197729}$.