To solve this problem, we need to understand how the investment and withdrawal processes interact over time. Linda-Anne's investment earns interest while withdrawals decrease the balance.

Step-by-Step Solution:

1. Identify the variables:

   • Initial investment: $P = 31,940$
   • Interest rate: $r = 15\%$ per annum, compounded quarterly $\Rightarrow \ r = \frac{15\%}{4} = 3.75\%$ per quarter.
   • Withdrawal every quarter: Starting with $W_1 = 791$
   • Each subsequent withdrawal decreases by 6%: $W_2 = 791 \times 0.94$, $W_3 = 791 \times 0.94^2$, and so on.

2. Determine the compound interest formula for growth with withdrawals: Since withdrawals occur every quarter, and the interest is also compounded quarterly, we must calculate the compound interest and then subtract the withdrawals.

   The formula for the account balance after each withdrawal is: $A_n = A_{n-1} \times (1 + r) - W_n$ where:

   • $A_n$ = balance after the $n$-th withdrawal.
   • $A_{n-1}$ = balance before the $n$-th withdrawal.
   • $r = 0.0375$ = interest per quarter.
   • $W_n = W_1 \times 0.94^{n-1}$ = the decreasing withdrawal amount.

3. Iterate the process for 28 quarters (7 years):

   • Since Linda-Anne is making withdrawals every 3 months, and 7 years equals 28 quarters, we need to calculate the balance after 28 withdrawals.
   • We begin with $A_0 = 31,940$ and proceed through each quarter, applying interest and then subtracting the withdrawal.

Let's proceed with these calculations. We will iterate over each quarter and update the balance accordingly.After 7 years, immediately following the last withdrawal, the balance in Linda-Anne's account will be R68,229.00.

Would you like more details on any part of this solution? Here are some related questions for further understanding:

1. How would the balance change if the interest rate were different?
2. What would happen if withdrawals were made monthly instead of quarterly?
3. How would the final balance be affected if each withdrawal decreased by a different percentage?
4. What if Linda-Anne started with a different initial investment amount?
5. How can we calculate the total amount withdrawn over the 7 years?

Tip: For problems involving compound interest with regular withdrawals, tracking changes for each period is key. A spreadsheet or iterative calculation helps to manage this effectively.