Question

On a $1 million line of credit for one year, a company has agreed to the following conditions: (A) accrue 0.92% monthly interest on any funds borrowed; (B) maintain a compensating balance of 6.98% of any funds borrowed; and (C) pay the accrued interest and the amount borrowed together at the end of the year. The company does not have excess cash and will need to borrow additional funds under the line of credit to keep the compensating balance. If the company needs $100,000 after setting aside the compensating balance, how much interest will it pay in total at the end of the year?

: $11,551 $11,863 $12,176 $12,488 $12,800

Answer 1

Given

Amount required after setting aside the Compensating balance = $ 100000

Compensating Balance = 6.98%

Interest = 0.92% accruing monthly interest

Computation of Amount required to be borrowed.

Amount required to be Borrowed = Amount needed after setting aside compensating balance / ( 1-Compensating balance %)

= $ 100000/ ( 1-6.98%)

= $ 100000/ 0.9302

= $ 107503.76

Hence Amount required to be borrowed is $ 107503.76

Given interest accrues monthly

Computation of Outstanding balance of the loan at the year end:

We know that Future value = Present value ( 1+i) ^n

Here I = Interest rate

n = No.of Compounding period

Since the Interest is compounded monthly hence the no.of times interest compounded in a year is 12*1 =12 times.

Outstanding loan = $ 107503.76( 1+0.0092) ^ 12

= $ 107503.76( 1.0092)^12

= $ 107503.76*1.11616

= $ 119991.40

Hence Outstanding loan balance is $ 119991.40

Computation of Interest amount

We know that Interest = Closing loan balance - Amount borrowed

= $ 119991.40- $ 107503.76

= $ 12488

Hence Interest at the year end is $ 12488.Hence option 4 is the Correct answer.

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