Sheila$$s Society Clothing Manufacturer has collection centres around the country to speed up cash collections. The company also makes its disbursements from remote disbursement centres, so cheques written by Sheila$$s take longer to clear the bank. Collection time has been reduced by two days and a half days and disbursement time has been increased by two days because of these policies. Excess funds are being invested in short$-$term instruments yielding $5$ percent per annum.

a$.$ If the firm has $$4\mathrm{.}50$ million per day in collections and $$3\mathrm{.}90$ million per day in disbursements, how many dollars has the cash management system freed up$?($Enter the answer in dollars not in millions.$)$

Freed$-$up funds $

b$.$ How much can Sheila$$s earn per year on short$-$term investments made possible by the freed$-$up cash? $($Enter the answer in dollars not in millions.$)$

Interest on freed$-$up cash $