Nth term of geometric series where each term is rounded to two decimal places

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I know that the nth term of a geometric series is

$$f(n, a_1) = a_n = a_1 r^{n-1}$$

In my case however, since I am dealing with money, I am rounding each term to two decimal places. I calculate the nth term using the previous term like so

$$ g(n, a_{n-1}) = a_n = round(a_{n-1}r) $$ where $$ a_1 = 1000; r = 1.000833333 $$

As you can see below, using $f$ will produce a discrepancy. For example, see below how rounding $f(2)$ will produce 1001.67 rather than 1001.66

n  f()          g()      
1  1000.833333  1000.83  
2  1001.667361  1001.66  

What is the formula to calculate the nth term of this geometric series where each term is rounded to two decimal places?