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Let's solve each part of the question.

---

### Part (a)
We need to determine the amount Andrew owed Sarah right before repaying $4000 on 1st January 2019.

**Step 1:** Initial Amount Borrowed

Andrew borrowed $21250 on 1st January 2018.

**Step 2:** Calculate Interest for 2018

On 31st December 2018, an interest of 4% was added to the amount owed.

\[
\text{Interest} = 0.04 \times 21250 = 850
\]

So, on 31st December 2018, the total amount owed by Andrew is:

\[
21250 + 850 = 22100
\]

**Step 3:** Repayment on 1st January 2019

Andrew repaid $4000 on 1st January 2019, which means the amount owed right after repayment was:

\[
22100 - 4000 = 18100
\]

Thus, before repaying $4000 on 1st January 2019, Andrew owed Sarah **$22100**, which matches the question’s requirement.

---

### Part (b)
Now, we need to calculate the amount Andrew owed after making another $4000 repayment on 1st January 2020.

**Step 1:** Calculate Interest for 2019

The balance on 1st January 2019 was $18100. An interest of 4% is applied on 31st December 2019.

\[
\text{Interest} = 0.04 \times 18100 = 724
\]

Adding this interest:

\[
18100 + 724 = 18824
\]

**Step 2:** Repayment on 1st January 2020

On 1st January 2020, Andrew repaid $4000, so the remaining balance is:

\[
18824 - 4000 = 14824
\]

Therefore, after the repayment on 1st January 2020, Andrew owed Sarah **$14824**.

---

Would you like further clarification on any of these steps, or do you have additional questions?

---

### Additional Related Questions
1. What would the debt be if the interest rate was different, say 5%?
2. How would the calculation change if Andrew repaid $5000 each year instead of $4000?
3. How would compound interest calculations differ in this context?
4. If Sarah stopped charging interest after a certain date, how would that affect the final amount owed?
5. How much total interest would Andrew end up paying if he continues to repay $4000 yearly?

### Tip
In financial calculations, always remember to apply interest before any repayments for the period, as interest typically accrues on the entire outstanding balance.

Andrew borrowed some money from Sarah. He borrowed $21,250 on 1st January 2018. On 31st December each year, starting on 31st December 2018, Sarah charged Andrew interest of 4% on the amount of money that he owed her. This interest was added to the amount of money that Andrew owed Sarah. On 1st January each year, starting on 1st January 2019, Andrew repaid $4,000 to Sarah.

(a) Show that before Andrew had repaid $4,000 to Sarah on 1st January 2019, he owed Sarah $22,100.

(b) After Andrew had repaid $4,000 to Sarah on 1st January 2020, calculate how much money Andrew now owed Sarah.

This problem involves calculating interest and annual repayments on a loan of $21,250 with a 4% interest rate. Learn how to calculate the total amount owed after each interest application and repayment, as well as determining the final amount owed after multiple repayments.

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