Jake invested R12500 on 1 January 2014 with a bank where interest was compounded at 14% p.a. quarterly until 1 July 2017 when the rate was changed to 12% p.a. compounded monthly.

a) What was the amount in the account on 1 July 2017?

b) What was the amount in the account on 1 October 2019?

c) How much interest did Jake earn during 2018?

d) Suppose Jake withdrew R15000 on 1 July 2018. What would the amount in the account be on 1 October 2019 and how many months after 1 October 2019 would he be able to withdraw as much as R15000 again?

e) How much could Jake withdraw on 1 July 2018 (instead of the R15000) so that there will be exactly R12000 in the account on 1 October 2019?

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 \( R 20,233.68 \).

---

### 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.

Jake invested R12500 on 1 January 2014 with a bank where interest was compounded at 14% p.a. quarterly until 1 July 2017 when the rate was changed to 12% p.a. compounded monthly.

a) What was the amount in the account on 1 July 2017?
b) What was the amount in the account on 1 October 2019?
c) How much interest did Jake earn during 2018?
d) Suppose Jake withdrew R15000 on 1 July 2018. What would the amount in the account be on 1 October 2019 and how many months after 1 October 2019 would he be able to withdraw as much as R15000 again?
e) How much could Jake withdraw on 1 July 2018 (instead of the R15000) so that there will be exactly R12000 in the account on 1 October 2019?

Learn how to calculate compound interest with rate changes over time, and see the impact of withdrawals on future balances. Jake invested R12500 at 14% p.a. quarterly compounded interest and faced a rate change to 12% p.a. compounded monthly. We explore the calculations for the amount on 1 July 2017, 1 October 2019, and during 2018. The problem also investigates how early withdrawals affect the final balance.

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