Compute a Year-End Balance with Monthly Card Fees

Problem Statement

You are given a starting bank balance and a history of transactions for the year 2020. Additionally, the bank charges a monthly card fee of $5 at the end of every month. The fee is waived for a given month if, within that month, the account processed at least 3 payments and the total spending across those payments exceeded $100.

Implement a function calculate_final_balance(initial_balance, transactions) where:

• initial_balance is a float.
• transactions is a list of dictionaries, each containing: amount (float), month (int, 1-12), and type (string, either "payment" or "deposit").

Rules

1. Payments decrease the balance; deposits increase it.
2. A "payment" is defined by the type field.
3. At the end of each month (1-12), calculate if the fee waiver applies based on the payments made during that specific month.
4. If the waiver does NOT apply, subtract $5 from the balance at the end of the month.
5. Return the balance after all transactions and monthly fees for December have been processed.

Example

# Input
initial_balance = 200.0
transactions = [
    {"amount": 50.0, "month": 1, "type": "payment"},
    {"amount": 30.0, "month": 1, "type": "payment"},
    {"amount": 40.0, "month": 1, "type": "payment"}
]
# Output: 195.0 
# Explanation: 3 payments in Jan total $120. Waiver applies (>=3 payments, >$100). 
# Balance = 200 - 50 - 30 - 40 = 80. Then fee is skipped. Wait, the example logic: 
# 200 - 120 = 80. No fee applied. Final balance 80.0.

Constraints

• initial_balance >= 0
• transactions list length is between 0 and 1000
• month is always between 1 and 12

Edge Cases

• Months with zero transactions.
• Months with payments but total spending under $100.
• Account balance dipping below zero (allowed).