### Minimum Yearly Repayment Calculation

To find the minimum yearly repayment (MYR) for the first year, we use the following values:
*   **Loan Balance ($P$):** $50,000
*   **Benchmark Interest Rate ($r$):** 8.77% = 0.0877
*   **Remaining Term ($n$):** 7 years

Using the formula:
$$MYR = \frac{P \times r}{1 - (1 + r)^{-n}}$$

**Step-by-step working:**
1. Calculate the numerator:
   $$50,000 \times 0.0877 = 4,385$$

2. Calculate the denominator:
   $$1 - (1 + 0.0877)^{-7} = 1 - (1.0877)^{-7}$$
   $$1.0877^{-7} \approx 0.55518293$$
   $$1 - 0.55518293 = 0.44481707$$

3. Divide the numerator by the denominator:
   $$MYR = \frac{4,385}{0.44481707} \approx 9,857.98399$$

**Minimum Yearly Repayment:** $9,857.98 (rounded to the nearest cent)

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### Controlling Authority
The controlling authority for the Division 7A minimum yearly repayment rule is the **Australian Taxation Office (ATO)**, under the *Income Tax Assessment Act 1936* (Cth).