A small construction firm, A&B Construction, is working on a house project for Mr. Long. The estimated building time is 8 months and the estimated costs to the firm (labor, materials, etc.) are $20,000 per month for 8 months (assume that the firm needs to pay the monthly costs at the end of each month). The contract indicates that the customer will pay a total of $200,000 for the project but it does not specify when the customer will pay the firm. To solve this problem, the firm offers to let the customer pay $50,000 in the end of each month for the first four months, but the customer offers to pay $23,000 in the end of each month for 8 months plus another payment of $16,000 when the project is completed. Assume that the firm would deposit all the earned money (profit) in a bank account earning a monthly interest rate of 0.476% (compounded monthly).

a) Conduct an analysis to estimate the difference in the firms total profit (i.e., bank account balance) at the end of the project between the firms offer and the customers offer . Note that the major objective of this project is to estimate what the difference between the two offers will be.