Let's solve the problem step by step.

Information given:

1. Initial investment: $R 12,500$ (on 1 January 2014)
2. Interest rates:
   • From 1 January 2014 to 1 July 2017: 14% p.a. compounded quarterly
   • From 1 July 2017 to 1 October 2019: 12% p.a. compounded monthly
3. Various points to calculate:
   • Amount on 1 July 2017
   • Amount on 1 October 2019
   • Interest earned during 2018
   • Impact of withdrawals and future balance.

We will start by solving each part.

Formula used:

The compound interest formula is:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $A$ is the final amount.
• $P$ is the principal (initial investment).
• $r$ is the annual interest rate (as a decimal).
• $n$ is the number of times interest is compounded per year.
• $t$ is the time in years.

a) Amount in the account on 1 July 2017

From 1 January 2014 to 1 July 2017, interest was compounded quarterly at 14% p.a. The duration is from 1 January 2014 to 1 July 2017, which is 3.5 years.

• Initial principal, $P = 12,500$
• Annual interest rate, $r = 14\% = 0.14$
• Quarterly compounding, $n = 4$
• Time period, $t = 3.5$ years

Let's calculate this amount first.The amount in the account on 1 July 2017 was approximately $R 20,233.68$.

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b) Amount in the account on 1 October 2019

From 1 July 2017 to 1 October 2019, the interest rate was changed to 12% p.a., compounded monthly. The time duration from 1 July 2017 to 1 October 2019 is 2.25 years (2 years and 3 months).

• Principal, $P = 20,233.68$ (amount from part (a))
• Annual interest rate, $r = 12\% = 0.12$
• Monthly compounding, $n = 12$
• Time period, $t = 2.25$ years

Let's calculate the amount on 1 October 2019.It seems like I can’t do more advanced data analysis right now. Please try again later.

In the meantime, you can continue with the following formula to calculate the amount for part (b):

$A = 20,233.68 \times \left(1 + \frac{0.12}{12}\right)^{12 \times 2.25}$

If you'd like to go through the rest of the parts or need more details, feel free to let me know.

Do you want me to assist further with these calculations, or would you prefer detailed explanations? Here are five related questions that may help:

1. How do you compute compound interest if compounding is continuous?
2. What happens when the interest rate changes during an investment period?
3. Can you explain the difference between nominal and effective interest rates?
4. How would the calculation change if the interest was compounded annually instead of quarterly or monthly?
5. How would early withdrawals affect the total interest earned?

Tip: When calculating compound interest, ensure that the time periods and compounding frequency align perfectly for accurate results.