BUG: Return decimal NaNs instead of TypeError

In case of infeasible/invalid problems npf.rate is supposed to return
nan. In cases where the required output is of type Decimal a TypeError
is raised instead as Decimal types do not support arithmatic with
floating point values. This PR uses a Decimal nan as required for the
error handling, returning a nan as expected.

See #14645

Author: mandeep-singh-sndk

numpy_financial/_financial.py

@@ -624,7 +624,7 @@ def rate(nper, pmt, pv, fv, when='end', guess=None, tol=None, maxiter=100):
         rn = rnp1
     if not close:
         # Return nan's in array of the same shape as rn
-        return np.nan + rn
+        return default_type(np.nan) + rn
     else:
         return rn
 

numpy_financial/tests/test_financial.py

@@ -9,6 +9,7 @@
     )
 
 import numpy_financial as npf
+import pytest
 
 
 class TestFinancial(object):
@@ -410,3 +411,30 @@ def test_broadcast_decimal(self):
                             [Decimal('-74.998201'), Decimal('-75.62318601'),
                              Decimal('-75.62318601'), Decimal('-76.88882405'),
                              Decimal('-76.88882405')], 4)
+
+    @pytest.mark.parametrize('number_type', [Decimal, float])
+    def test_rate_nan(self, number_type):
+        """
+        Test for checking inputs whose output is NaN
+        Rate will return NaN, if newton raphson method's change or diff was not able to become
+        less than default tolerance value i.e. 1e-6 in max iterations possible,
+        Both payments and present value are positive, it is impossible to pay off the existing balance
+        by making further withdrawals, regardless of the rate.
+        """
+        rate = npf.rate(number_type(12.0), number_type('400.0'), number_type('10000.0'), number_type(0))
+        assert_equal(numpy.nan, float(rate))
+        rate = npf.rate(number_type(12.0), number_type('400.0'), number_type('10000.0'), number_type(5000))
+        assert_equal(numpy.nan, float(rate))
+
+        # begin
+        rate = npf.rate(number_type(12.0), number_type('400.0'), number_type('10000.0'), number_type(20000), 1)
+        assert_equal(numpy.nan, float(rate))
+        rate = npf.rate(number_type(12.0), number_type('400.0'), number_type('10000.0'), number_type(20000), 'begin')
+        assert_equal(numpy.nan, float(rate))
+
+        # end
+        rate = npf.rate(number_type(12.0), number_type('400.0'), number_type('10000.0'), number_type(0))
+        assert_equal(numpy.nan, float(rate))
+        rate = npf.rate(number_type(12.0), number_type('400.0'), number_type('10000.0'), number_type(0), 'end')
+        assert_equal(numpy.nan, float(rate))
+