"Unorderable types: int() < str()"

The issue here is that input() returns a string in Python 3.x, so when you do your comparison, you are comparing a string and an integer, which isn't well defined (what if the string is a word, how does one compare a string and a number?) - in this case Python doesn't guess, it throws an error.

To fix this, simply call int() to convert your string to an integer:

int(input(...))

As a note, if you want to deal with decimal numbers, you will want to use one of float() or decimal.Decimal() (depending on your accuracy and speed needs).

Note that the more pythonic way of looping over a series of numbers (as opposed to a while loop and counting) is to use range(). For example:

def main():
    print("Let me Retire Financial Calculator")
    deposit = float(input("Please input annual deposit in dollars: $"))
    rate = int(input ("Please input annual rate in percentage: %")) / 100
    time = int(input("How many years until retirement?"))
    value = 0
    for x in range(1, time+1):
        value = (value * rate) + deposit
        print("The value of your account after" + str(x) + "years will be $" + str(value))

Just a side note, in Python 2.0 you could compare anything to anything (int to string). As this wasn't explicit, it was changed in 3.0, which is a good thing as you are not running into the trouble of comparing senseless values with each other or when you forget to convert a type.