# Division 7A minimum yearly repayment - first year

*This is a benchmarking hypothetical, not tax advice. Figures are as at FY2025-26.*

## Answer

**Minimum yearly repayment (first year): $9,857.98**

**Controlling authority:** Section 109E of the *Income Tax Assessment Act 1936* (Cth)
- specifically the minimum yearly repayment formula in **s 109E(6)**, applied through the
amount-of-repayment rule in **s 109E(5)** and the benchmark interest rate definition in
**s 109N(2)**. Division 7A itself is Division 7A of Part III of the ITAA 1936 (ss 109B-109ZE).

## Working

The minimum yearly repayment fully amortises the loan over the remaining term at the
benchmark rate:

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

Inputs:

| Symbol | Meaning | Value |
|--------|---------|-------|
| `P` | loan balance | $50,000 |
| `r` | Division 7A benchmark interest rate | 8.77% = 0.0877 |
| `n` | remaining loan term (years) | 7 |

Step by step:

1. Numerator: `P × r = 50,000 × 0.0877 = 4,385.00`
2. `(1 + r)^-n = (1.0877)^-7 = 0.555182924512...`
3. Denominator: `1 - (1.0877)^-7 = 0.444817075487...`
4. `MYR = 4,385.00 / 0.444817075487... = 9,857.98486983...`
5. Rounded to the nearest cent: **$9,857.98**

(High-precision check: `MYR = 9857.98486983359...`, which rounds to $9,857.98.)

## Note on approach

- Applied the amortising-annuity formula exactly as given in the task, with `P = 50,000`,
  `r = 0.0877`, `n = 7`. This is the standard form of the Division 7A minimum yearly
  repayment: the constant payment that pays the loan down to nil over the remaining term
  at the benchmark rate.
- Computed the figure both with double-precision floating point and with 50-digit decimal
  arithmetic; both give `9857.98486983...`, so the cent rounding is unambiguous
  ($9,857.98, not $9,857.99).
- The benchmark rate (8.77%) and the 7-year unsecured maximum term used here match the
  FY2025-26 Division 7A settings stated in the task.
- On authority: the operative rule for the minimum yearly repayment lives in s 109E of the
  ITAA 1936. The loan is taken to be a dividend (s 109E(1)) unless the borrower makes at
  least the minimum yearly repayment, the amount of which is set by the formula in
  s 109E(6); s 109N sets the complying-loan conditions (maximum term and benchmark rate).
  The benchmark rate is the "indicator lending rates - bank variable housing loans interest
  rate" last published by the RBA before the start of the income year, as picked up by
  s 109N(2).