Question: An incorrect evaluation of a function at a point

As a new user of Maple (Maple 2015), I defined the function:

f:=x->(1+1/x)^x

As x->infinity, f(x) increases monotonically to e, as is known.

In financial applications, this function and related functions are often used to show that periodic compounding converges to continuous compounding as the number of compounding periods grows larger.

However, for certain large values of x, f(x) evaluates to functional values larger than e.  For example:

f(x)|x=31536000. evaluates to 2.74327....

which is greater than e=2.71828...

Also notice that is(f(31536000.)>e) returns true.

This incorrect evaluation makes it difficult to demonstrate to students the principles of and relationship between periodic compounding and continuous compounding.

Some other CAS (Mathematica and HP Prime) evaluate the function correctly while TI Nspire also evaluates the function incorrectly.

The following file demonstrates this behavior of Maple 2015:

20160705_example_of_function_evaluation_issue.mw

Can anyone share any insight to this issue or any errors that I am making.