Question

?You plan to borrow ?$50,000 from the bank to pay for inventories for a gift shop you have just opened. The bank offers to lend you the money at 11 percent annual interest for the 9 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 16 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?

Answer 1

The answers to the questions are as follows -

a. Annualised rate of interest = 11% x (No. of months loan / 12 months) = 11 x (9/12) = 8.25%

b. Since the compensating balance required to be maintained is 16%, the amount that will be disbursed by the bank as loan will be $ 50,000 x (100-16)% = $ 42,000.

Interest to be paid on the loan = $ 50,000 x 11% x (9/12) = $ 4,125

Therefore, cost of loan now (annualised) = (4,125/42,000) x 100 = 9.82% {Since only $ 42,000 is available for use, cost is to be calculated on that component only}

c. In case of interest discounting, the interest of $ 4,125 will be deducted from the loan disbursement itself. So effectively the disbursement = $ 42,000 - $ 4,125 = $ 37,875

So annualised interest now = (4,125/37,875) x 100 = 10.89%