Reject loan offers that can never amortise

At high rate and long duration the rounded instalment converges to C*i from
above and lands exactly on the first month's interest, leaving zero principal:
at 99 % the frontier is 294 months for the maximum capital. The schedule would
never terminate.

Checking the first month suffices: once principal is positive the outstanding
capital decreases, so interest decreases and principal grows. The check must
stay after the bounds checks, since it calls monthly_repayment() and that
function's expect() is justified by them.

creating_loan_offer_with_limit_inputs_works asserted that the three maxima
combined were valid, which this invariant makes false. The valid domain is no
longer a box. It is replaced by the corner that actually maximises the
instalment, duration 1, at 1 082 499 999,99 EUR against 82 500 000,00 EUR for
the corner it tested before.

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

crates/immo-core/src/loan_offer.rs

@@ -18,6 +18,8 @@ pub enum LoanOfferError {
     MaxAnnualNominalRateExceeded(Decimal),
     #[error("loan duration in months should be lower than {MAX_LOAN_DURATION_IN_MONTHS}: {0}")]
     MaxLoanDurationExceeded(u64),
+    #[error("loan cannot amortise")]
+    LoanCannotAmortise,
 }
 
 /// 1b€ is a pretty expensive house...
@@ -59,11 +61,21 @@ impl LoanOffer {
         } else if borrowed_capital > MAX_BORROWED_CAPITAL {
             Err(LoanOfferError::MaxBorrowedCapitalExceeded(borrowed_capital))
         } else {
-            Ok(LoanOffer {
+            let loan_offer = LoanOffer {
                 borrowed_capital,
                 annual_nominal_rate,
                 loan_duration_in_months,
-            })
+            };
+            // Check that the first month is not "only interests", otherwise the loan cannot be reimbursed
+            // /!\ Must be kept after all the previous verifications otherwise monthly_repayment() can panic
+            if loan_offer.monthly_repayment().as_decimal()
+                > (borrowed_capital.as_decimal() * loan_offer.proportional_monthly_interest_rate())
+                    .round_dp(2)
+            {
+                Ok(loan_offer)
+            } else {
+                Err(LoanOfferError::LoanCannotAmortise)
+            }
         }
     }
 
@@ -98,7 +110,7 @@ mod tests {
 
     #[test]
     fn creating_loan_offer_with_negative_interest_rate_returns_negative_interest_rate_error() {
-        let ret = LoanOffer::new(Euros::from_cents_as_i64(123), Decimal::new(-45, 2), 5);
+        let ret = LoanOffer::new(Euros::from_cents_as_i64(123), Decimal::new(-45, 2), 60);
         assert_eq!(
             ret,
             Err(LoanOfferError::NegativeInterestRate(Decimal::new(-45, 2)))
@@ -177,6 +189,16 @@ mod tests {
         );
     }
 
+    #[test]
+    fn creating_loan_offer_that_cannot_amortise_returns_loan_cannot_amortise_error() {
+        let ret = LoanOffer::new(
+            Euros::from_cents_as_i64(439_000_00),
+            Decimal::new(99, 2),
+            480,
+        );
+        assert_eq!(ret, Err(LoanOfferError::LoanCannotAmortise));
+    }
+
     #[test]
     fn creating_loan_offer_with_correct_inputs_works() {
         let ret = LoanOffer::new(Euros::from_cents_as_i64(10), Decimal::new(45, 2), 15);
@@ -191,12 +213,8 @@ mod tests {
     }
 
     #[test]
-    fn creating_loan_offer_with_limit_inputs_works() {
+    fn creating_loan_offer_with_max_repayment_works() {
-        let ret = LoanOffer::new(
+        let ret = LoanOffer::new(MAX_BORROWED_CAPITAL, MAX_ANNUAL_NOMINAL_RATE, 1);
-            MAX_BORROWED_CAPITAL,
-            MAX_ANNUAL_NOMINAL_RATE,
-            MAX_LOAN_DURATION_IN_MONTHS,
-        );
         assert!(ret.is_ok());
         // Should not panic - checks that expect assertion is valid
         ret.unwrap().monthly_repayment();
@@ -219,11 +237,11 @@ mod tests {
     fn conversion_to_annual_nominal_rate_in_percent_works() {
         let offer = LoanOffer::new(
             Euros::from_cents_as_i64(150_000_00),
-            Decimal::new(4, 4),
+            Decimal::new(4, 2),
             300,
         )
         .unwrap();
-        assert_eq!(offer.annual_nominal_rate_in_percent(), Decimal::new(4, 2));
+        assert_eq!(offer.annual_nominal_rate_in_percent(), Decimal::new(400, 2));
     }
 
     #[test]