Multiplying Product Via Loop in R

I want to multiply all the element in the fact vector,
namely:

final_prod = 0.01 * 0.05 * 0.02
 

This is how I do it in loop.

fact <- c(0.01,0.05,0.02)
 
 final_prod <- 1;
 for (i in 1:range(fact)){
    all_prod <- all_prod * fact[i];
 }
 
 print(final_prod)
 

But the final product it gave is wrong. It should be
0.00001 instead of 0.01.

What's wrong with my approach above?

I understand there is R'ish way. But the reason
I want to do it in loop is because there is more complex
computation involved.

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