Product and Round a series of numbers

Hi All,

I have to do this kind of calculation quite often and i would like to know if there is a shortcut out there somewhere. The scenario is that i would like to multiply 2 numbers together then round to the nearest penny, then multiply that value by another number and round to the nearest penny, and continue this pattern on for a set amount of numbers. Mind you the end value will sometimes be different than just multiplying all of the numbers together then rounding at the end. Here is an example:

Column A
1.19
1.11
1.86
1.47
1.36
1.09
1.78
1.02
1.20

If you were to do this formula round(product(A2:A10),2) you would come up with 11.66, but i would like the value that is calculated from this formula:
=ROUND(ROUND(ROUND(ROUND(ROUND(ROUND(ROUND(ROUND(A2*A3,2)*A4,2)*A5,2)*A6,2)*A7,2)*A8,2)*A9,2)*A10,2) which would be 11.68

This number can be significatly different if the numbers that you are looking at have more than two decimal places. I am looking for a formula, if at all possible, that will do what i have shown just must shorter. Thanks in advance for any assistance.