import calendar
from dataclasses import dataclass
from datetime import date
from decimal import ROUND_HALF_UP, Decimal

CENT = Decimal("0.01")


@dataclass(frozen=True)
class Installment:
    due: date
    payment: Decimal
    interest: Decimal
    principal: Decimal
    remaining: Decimal


def add_months(d: date, months: int) -> date:
    y, m0 = divmod(d.year * 12 + d.month - 1 + months, 12)
    m = m0 + 1
    return date(y, m, min(d.day, calendar.monthrange(y, m)[1]))


def annuity_payment(principal: Decimal, annual_rate_pct: Decimal, term_months: int) -> Decimal:
    i = annual_rate_pct / Decimal(100) / Decimal(12)
    if i == 0:
        return (principal / term_months).quantize(CENT, ROUND_HALF_UP)
    q = (Decimal(1) + i) ** term_months
    return (principal * i * q / (q - Decimal(1))).quantize(CENT, ROUND_HALF_UP)


def loan_schedule(principal: Decimal, annual_rate_pct: Decimal, term_months: int,
                  payout_date: date, repayment_type: str) -> list[Installment]:
    i = annual_rate_pct / Decimal(100) / Decimal(12)
    plan: list[Installment] = []
    remaining = principal
    if repayment_type == "bullet":
        for n in range(1, term_months + 1):
            interest = (remaining * i).quantize(CENT, ROUND_HALF_UP)
            principal_part = remaining if n == term_months else Decimal("0")
            remaining = remaining - principal_part
            plan.append(Installment(add_months(payout_date, n),
                                    -(interest + principal_part), interest,
                                    principal_part, remaining.quantize(CENT)))
        return plan
    rate = annuity_payment(principal, annual_rate_pct, term_months)
    for n in range(1, term_months + 1):
        interest = (remaining * i).quantize(CENT, ROUND_HALF_UP)
        principal_part = rate - interest
        if n == term_months or principal_part > remaining:
            principal_part = remaining
        remaining = remaining - principal_part
        plan.append(Installment(add_months(payout_date, n),
                                -(interest + principal_part), interest,
                                principal_part, remaining.quantize(CENT)))
    return plan