Annual vs monthly cost calculator

month_vs_year_calc.py

def calc_rate_offset(monthly_cost, annual_cost, tolerance=1e-8):
    """
    Find the monthly interest rate needed to offset the cost difference
    between monthly and annual plans.
    """
    total_monthly = 12 * monthly_cost
    diff = total_monthly - annual_cost  # Extra cost to offset

    # If there's no meaningful difference, no interest rate is needed
    if diff <= 0:
        print("Monthly plan is cheaper or equal to the annual plan.")
        return 0.0

    # Binary search bounds
    lower_rate = 0.0
    upper_rate = 1.0
    best_rate = None
    min_diff = float("inf")
    iteration = 0  # Track iterations for debugging

    def debug_output(iteration, lower, upper, mid, balance, interest_earned):
        """Optional: Print debug information for each iteration."""
        print(f"Iteration {iteration}:")
        print(
            f"  Lower Rate: {lower:.6f}, Upper Rate: {upper:.6f}, Mid Rate: {mid:.6f}"
        )
        print(
            f"  Final Balance: {balance:.2f}, Total Interest Earned: {interest_earned:.2f}, Target: {diff:.2f}"
        )

    # Binary search loop
    while upper_rate - lower_rate > tolerance:
        mid_rate = (lower_rate + upper_rate) / 2
        balance = total_monthly
        total_interest = 0.0

        # Simulate monthly accrual and deductions
        for month in range(12):
            interest = balance * mid_rate
            total_interest += interest
            balance += interest - monthly_cost

        # Check if this rate is the closest to the target difference
        current_diff = abs(total_interest - diff)
        if current_diff < min_diff:
            min_diff = current_diff
            best_rate = mid_rate

        # Debugging: Report balance and rate bounds
        debug_output(
            iteration, lower_rate, upper_rate, mid_rate, balance, total_interest
        )

        # Adjust rate bounds based on final balance
        if total_interest > diff:
            upper_rate = mid_rate
        else:
            lower_rate = mid_rate

        iteration += 1

    monthly_after_interest = total_monthly - total_interest
    # Summary
    print("\nSummary:")
    print(f"  Total Interest Earned: {total_interest:.2f}")
    print(f"  Total Monthly Cost After Interest Offset: {monthly_after_interest:.2f}")
    print(f"  Cost Difference: {diff:.2f}")
    print(f"  Annual Cost: {annual_cost:.2f}")
    print(f"\nSearch completed in {iteration} iterations.")
    return best_rate


try:
    monthly_cost = float(input("Enter the monthly subscription cost: "))
    annual_cost = float(input("Enter the annual subscription cost: "))

    required_interest_rate = calc_rate_offset(monthly_cost, annual_cost)
    if required_interest_rate is not None:
        annual_interest_rate = (1 + required_interest_rate) ** 12 - 1
        print(f"Annual Interest Rate: {annual_interest_rate * 100:.3f}%")
        print(f"Monthly Interest Rate: {required_interest_rate * 100:.4f}%")

    else:
        print("No valid interest rate found.")
except ValueError:
    print("Invalid input. Please enter numeric values.")