## Minimum yearly repayment — first year

**Formula:**

MYR = P × r / (1 − (1 + r)⁻ⁿ)

**Inputs:**
- P = $50,000
- r = 8.77% = 0.0877
- n = 7 years

**Working:**

1. (1 + r)ⁿ = 1.0877⁷ ≈ 1.8012081
2. (1 + r)⁻ⁿ = 1 / 1.8012081 ≈ 0.5551829
3. Denominator: 1 − 0.5551829 = 0.4448171
4. Numerator: 50,000 × 0.0877 = 4,385.00
5. MYR = 4,385.00 / 0.4448171 ≈ **$9,857.98**

**Minimum yearly repayment for the first year: $9,857.98**

## Controlling authority

The controlling authority is **section 109E of the Income Tax Assessment Act 1936 (Cth)** (within Division 7A of Part III), which imposes the minimum yearly repayment requirement and sets out the amortisation formula in s 109E(5). The benchmark interest rate used in that formula is defined in **s 109N(2)** of the same Act (by reference to the rate published by the ATO).