**Minimum yearly repayment calculation**

MYR = P × r / (1 − (1 + r)^(−n)), with P = 50000, r = 0.0877, n = 7.

(1.0877)^7 = 1.80120813  
(1.0877)^(−7) = 1 / 1.80120813 ≈ 0.55518292  
1 − 0.55518292 = 0.44481708  
0.0877 / 0.44481708 ≈ 0.19715970  
50000 × 0.19715970 = 9857.985  

Rounded to nearest cent: 9857.98.

The minimum yearly repayment for the first year is 9857.98 dollars.

The controlling authority for the Division 7A minimum yearly repayment rule is the Australian Taxation Office (ATO).