Currently Jean has R10450 in a bank account which earns interest at i(4) = 0.17 p.u.p.a.
a) How much can he withdraw today if he wants R12000 in the account in two years’ time?
b) What amount can he withdraw in exactly 12 months if he wants R10000 in the account three years from today?

We can solve both parts of the problem using the formula for compound interest:

\[
A = P \left( 1 + \frac{i}{m} \right)^{mt}
\]

Where:
- \(A\) is the future value (the amount Jean wants in the account in the future),
- \(P\) is the present value (the current amount in the account),
- \(i\) is the nominal annual interest rate (17% or 0.17),
- \(m\) is the compounding frequency (4 times per year, since it's quarterly compounded),
- \(t\) is the time in years.

### Part a: Withdraw today (2 years from now, wants R12000)

Here, Jean wants R12000 in the account two years from now. Let's denote the amount he can withdraw today as \(W\). This implies the present value \(P\) that remains after the withdrawal is:

\[
P = 10450 - W
\]

We can use the compound interest formula to find \(P\), knowing that \(A = 12000\), \(i = 0.17\), \(m = 4\), and \(t = 2\):

\[
12000 = (10450 - W) \left( 1 + \frac{0.17}{4} \right)^{4 \times 2}
\]

Now, solving for \(W\).

### Part b: Withdraw in exactly 12 months (wants R10000 in 3 years)

In this case, Jean wants R10000 in the account three years from today. He will make a withdrawal after 12 months. The amount in the account after the withdrawal will accumulate for the remaining two years.

Let's denote the withdrawal amount in 12 months as \(W_1\), and the amount left in the account after the withdrawal as \(P_1 = 10450(1 + \frac{0.17}{4})^{4 \times 1} - W_1\). This amount will grow to R10000 in two more years.

Using the compound interest formula for the amount left after the first year:

\[
10000 = P_1 \left( 1 + \frac{0.17}{4} \right)^{4 \times 2}
\]

I'll calculate both parts step by step.

### Let's begin with part a.For part (a), Jean can withdraw approximately R1848.53 today if he wants to have R12000 in the account in two years' time.

Now, let's move on to part (b) and calculate the withdrawal after 12 months to leave R10000 in the account three years from today.It seems like I can’t do more advanced data analysis right now. Please try again later.

Feel free to reach out if you'd like help with other parts of this or a new question!

Here are five questions related to this topic:
1. How does the compounding frequency affect the final amount in a compound interest calculation?
2. What would happen if the interest rate was compounded annually instead of quarterly?
3. How would the withdrawal change if Jean wanted R15000 in the account instead of R12000?
4. What if Jean wanted to make smaller withdrawals every six months? How would that be calculated?
5. How does inflation impact the value of Jean’s withdrawals in real terms?

**Tip:** When calculating compound interest, remember that higher compounding frequencies increase the amount of interest earned over time.

This detailed solution helps calculate how much Jean can withdraw today or in 12 months from his bank account, which earns quarterly compounded interest at 17% p.a. Learn the steps using the compound interest formula to find the required withdrawal amounts, suitable for Grades 11-12.

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