$($Related to Checkpoint $18\mathrm{.}2)($Calculating the cost of short$-$term financing$)$ The R$.$ Morin Construction Company needs to borrow $$100,000$ to help finance the cost of a new $$150,000$ hydraulic crane used in the firm's commercial construction business. The crane will pay for itself in one year, and the firm is considering the following alternatives for financing its purchase:

Alternative A$.$ The firm's bank has agreed to lend the $$100,000$ at a rate of $13$ percent. Interest would be discounted, and a $15$ percent compensating balance would be required. However, the compensating$-$balance requirement is not binding on the firm because it normally maintains a minimum demand deposit $($checking account$)$ balance of $$25,000$ in the bank.

Alternative B$.$ The equipment dealer has agreed to finance the equipment with a $1-$year loan. The $$100,000$ loan requires payment of principal and interest totaling $$116,420.$

a$.$ Which alternative should Morin select?

b$.$ If the bank's compensating$-$balance requirement had necessitated idle demand deposits equal to $15$ percent of the loan, what effect would this have had on the cost of the bank loan alternative?

a$.$ The cost of Alternative A would be $\%.($Round to two decimal places.$)$