The aninual Exercise Club membership fees of $\$ 1750$ are due on January 18,2018 Club management offers a reduction of membership fees of $187 \%$ p a to members who pay the dues by December 29,2017 How much must a member pay on December 29,2017 , if she chooses to take advantage of the club management's offer?
She must pay $\$ \square$
(Round the final answer to the nearest cent as reeded Round all intermediate values to six decimal places as needed)

Step 1 ：The problem is asking for the amount a member must pay if she chooses to take advantage of the club management's offer. The offer is a reduction of membership fees of 187% per annum. This means that for every year, the member gets a reduction of 187% on the membership fee. However, the member is paying the fee early, specifically 20 days early (from December 29, 2017 to January 18, 2018). Therefore, we need to calculate the reduction for these 20 days.

Step 2 ：The formula to calculate the reduction is: \(\text{Reduction} = \text{Principal} \times \text{Rate} \times \text{Time}\) where: Principal is the original amount of the membership fee ($1750), Rate is the reduction rate (187% per annum or 1.87 per year), Time is the time period for which the reduction is calculated (20 days out of 365 days in a year).

Step 3 ：Substitute the given values into the formula: \(\text{Reduction} = 1750 \times 1.87 \times 0.0547945205479452 = 179.31506849315068\)

Step 4 ：We then subtract this reduction from the original membership fee to get the amount the member must pay: \(\text{Amount to pay} = 1750 - 179.31506849315068 = 1570.6849315068494\)

Step 5 ：Final Answer: She must pay \(\boxed{1570.68}\)