## Minimum yearly repayment (first year)

**$9,857.98**

### Working

Given:

- Loan balance \(P\) = $50,000  
- Benchmark rate \(r\) = 8.77% = 0.0877  
- Remaining term \(n\) = 7 years  

Minimum yearly repayment (MYR) fully amortises the loan at the benchmark rate:

\[
\text{MYR} = \frac{P \times r}{1 - (1 + r)^{-n}}
\]

Numerator: \(50{,}000 \times 0.0877 = 4{,}385.00\)

Denominator: \(1 - (1.0877)^{-7} = 1 - 0.555337 \approx 0.444663\)

\[
\text{MYR} = \frac{4{,}385.00}{0.444663} = 9{,}857.98487\ldots
\]

Rounded to the nearest cent: **$9,857.98**.

### Controlling authority

The Division 7A minimum yearly repayment rule is set by **Division 7A of Part III of the *Income Tax Assessment Act 1936* (ITAA 1936)**, in particular **section 109E**, which defines how the minimum yearly repayment is calculated for complying loans so that principal and benchmark interest are repaid over the maximum term of the loan.

---

*Benchmarking hypothetical, not tax advice.*

### Approach

Applied the amortisation formula from the task using \(P = 50{,}000\), \(r = 0.0877\), and \(n = 7\), then rounded to the nearest cent. Named the ITAA 1936 Division 7A provision that governs minimum yearly repayments on complying loans.