$($Related to Checkpoint $18\mathrm{.}3)($Calculating the cost of short$-$term financing$)$You plan to borrow $$40,000$ from the bank to pay for inventories for a gift shop you have just opened. The bank offers to lend you the money at $13$ percent annual interest for the $3$ 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 $16$ 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 $12$ 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?

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Part $1$

a$.$The effective rate of interest, or APR, on the loan is

$$

$\%?($Round to two decimal places.$)$

Part $2$

b$.$If the bank requires you to maintain a compensating balance of $16$ percent in the bank, the effective annual cost of the loan now is

$$

$\%?($Round to two decimal places.$)$

Part $3$

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

$$

$\%?($Round to two decimal places.$)$