Step 1 :Given that the principal amount (P) is $3641, the rate of interest (R) is 3% or 0.03, and the time (T) is 10 months or approximately 0.833 years.
Step 2 :We can calculate the simple interest (I) using the formula I = PRT.
Step 3 :Substituting the given values into the formula, we get I = 3641 * 0.03 * 0.833.
Step 4 :Calculating the above expression, we find that I = 91.02499999999999.
Step 5 :Rounding to the nearest cent, we get the final simple interest as $91.03.
Step 6 :\(\boxed{91.03}\) dollars is the final answer.