feat: Kredit-Mathematik (Annuitaet, endfaellig)

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

finance/app/engine/loans.py

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+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