Microbiotics currently sells all of its frozen dinners cash$-$on$-$delivery but believes it can increase sales by offering supermarkets $1$ month of free credit. The price per carton is $$180,$ and the cost per carton is $$105.$ The unit sales will increase from $1,130$ cartons to $1,190$ per month if credit is granted. Assume all customers pay their bills and take full advantage of any credit period offered.

a$.$ If the interest rate is $1\%$ per month, what will be the change in the firm's total monthly profits on a present value basis if credit is offered to all customers?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

b$.$ If the interest rate is $1\mathrm{.}5\%$ per month, what will be the change in the firm's total monthly profits on a present value basis if credit is offered to all customers?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places. Negative amount should be indicated by a minus sign.

c$.$ Assume the interest rate is $1\mathrm{.}5\%$ per month but the firm can offer the credit only as a special deal to new customers, while existing customers will continue to pay cash on delivery. What will be the change in the firm's total monthly profits on a present value basis under these conditions?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

a$.$ Change in total monthly profit

b$.$ Change in total monthly profit

c$.$ Change in total monthly profit