Question

You've worked out a line of credit arrangement that allows you to borrow up to $55 million at any time. The interest rate is 0.65 percent per month. In addition, 3 percent of the amount that you borrow must be deposited in a non-interest-bearing account. Assume that your bank uses compound interest on its line of credit loans.

  

Required:

(a)	What is the effective annual interest rate on this lending arrangement? (Do not round your intermediate calculations.)
	(Click to select)8.34%8.19%8.68%8.08%11.26%

  

(b)	Suppose you need $13 million today and you repay it in 9 months. How much interest will you pay? (Do not round your intermediate calculations.)
	(Click to select)14,341,393.47780,575.831,206,779.21-12,999,900.00804,717.35

Answer 1

Given Rate of interest = 0.65% per month

We know that Effective Annual interest= ( 1+i)^n -1

Here I = Interest rate per period

n = No.of Compounding periods in a year

a) Computation of Effective annual rate

Effective Annual interest = ( 1+0.0065)^12 -1

= ( 1.0065)^12 - 1

= 1.08085-1

= 0.08085 or 8.085%

Effective Annual rate without Compensating balance is 8.085%

We also know that Effective Annual rate with Compensatingbalance = Effective Annual rate without compensating balance / ( 1-Non interest bearing deposit rate)

= 8.085% / ( 1-0.03)

= 8.085% /0.97

= 0.083351

EffectiveAnnual rate on the lending arrangement iss 8.34%. Hence option 1 is correct.

Computation of Amount to be borrowed

Required amount = $ 130,00000

Compenstaing Balance = 3%

Amount to be Borrowed = Required amount / ( 1- Compensating balance )

= $ 130,00000/ ( 1-0.03)

= $ 130,00000/0.97

= $ 13402061.86

Hence the amount to be borrowed is $ 13402061.86

b)Computation of interest amount

Computation of Outstandinng balance on the loan

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

Here I = Interest rate per period

n = No.of payments

Future value =$ 13402061.86( 1+0.0065)^9

= $ 13402061.86( 1.0065)^9

= $ 13402061.86*1.060044

= $ 14206775.26

Interest amount = Outstanding balance -loan amount

= $ 14206775.26-$ 13402061.86

= $ 804713.4

Hence the interest amount is $ 804713.4. Interest amount is within the range$ 206779.21-$ 12999900.

If you are having any doubts,please post a comment.

Thank you.please rate it.