Final answer:
The recursive formula for the balance Aₙ is Aₙ = 1.005833 ⋅ Aₙ₋₁ - 1796.33, with the initial balance A₀ of $270,000.
Step-by-step explanation:
The student has provided the initial balance A₀ of $270,000 and is looking for a recursive formula for their balance Aₙ with a monthly interest rate calculation. Since the interest is compounded monthly, the rate per period is ⅘.07∙12 = 0.005833 (or 0.5833%). We use the given recursive relationship Aₙ = (1 + (0.07∙12)) ⋅ Aₙ₋₁ - 1796.33, with each subsequent balance being the previous month's balance multiplied by 1.005833 and then subtracting the monthly payment of $1796.33.
To represent this as a general formula:
- Initial balance (A₀): $270,000
- Recursive formula (Aₙ): Aₙ = 1.005833 ⋅ Aₙ₋₁ - 1796.33, for n > 0