$($Related to Checkpoint $18\mathrm{.}3)($Calculating the cost of short$-$term financing$)$ You plan to borrow $$20,000$ from the bank to pay for inventories for a gift shop you have just opened. The bank

offers to lend you the money at $8$ percent annual interest for the $6$ months the funds will be needed $($assume a $360-$day year$).$

a$.$ Calculate the annualized rate of interest on the loan.

b$.$ In addition, the bank requires you to maintain a $20$ percent compensating balance in the bank. Because you are just opening your business, you do not have a demand deposit account at

the bank that can be used to meet the compensating$-$balance requirement. This means that you will have to put $20$ percent of the loan amount $($which you had planned to use to help finance

the business$)$ in a checking account. What is the cost of the loan now?

c$.$ In addition to the compensating$-$balance requirement in part b$,$ you are told that interest will be discounted. What is the annualized rate of interest on the loan now?