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

finance/tests/test_loans.py

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+from datetime import date
+from decimal import Decimal
+
+from app.engine.loans import add_months, annuity_payment, loan_schedule
+
+
+def test_add_months_clamps_month_end():
+    assert add_months(date(2026, 1, 31), 1) == date(2026, 2, 28)
+
+
+def test_annuity_payment():
+    # 10.000 EUR, 6 % p.a., 48 Monate -> 234,85 EUR Monatsrate
+    assert annuity_payment(Decimal("10000"), Decimal("6"), 48) == Decimal("234.85")
+
+
+def test_annuity_schedule_amortizes_fully():
+    plan = loan_schedule(Decimal("10000"), Decimal("6"), 48, date(2026, 8, 1), "annuity")
+    assert len(plan) == 48
+    assert plan[-1].remaining == Decimal("0.00")
+    assert plan[0].due == date(2026, 9, 1)
+    assert plan[0].interest == Decimal("50.00")  # 10000 * 0,5 %
+    assert plan[0].payment < 0
+
+
+def test_bullet_loan():
+    plan = loan_schedule(Decimal("10000"), Decimal("6"), 12, date(2026, 8, 1), "bullet")
+    assert all(i.principal == 0 for i in plan[:-1])
+    assert plan[-1].principal == Decimal("10000")
+    assert plan[-1].remaining == Decimal("0.00")