Minimum yearly repayment calculation

Given:
P = $50,000
r = 8.77% = 0.0877
n = 7 years

Formula:
MYR = P * r / (1 - (1 + r)^-n)

Step 1 - compute (1 + r)^n:
(1.0877)^7 = 1.80120814

Step 2 - compute (1 + r)^-n:
(1.0877)^-7 = 1 / 1.80120814 = 0.55518292

Step 3 - compute the denominator:
1 - 0.55518292 = 0.44481708

Step 4 - compute the numerator:
P * r = 50,000 * 0.0877 = 4,385.00

Step 5 - divide:
MYR = 4,385.00 / 0.44481708 = 9,857.98

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

Controlling authority: Section 109E of the Income Tax Assessment Act 1936 (Cth) - this section sets out the Division 7A minimum yearly repayment rule (including the amortisation formula and the consequence that a shortfall is treated as an unfranked dividend). The benchmark interest rate used in the formula is set annually by the Commissioner of Taxation (ATO) by Taxation Determination.