A firm borrowed $1,500,000 from National Bank. The loan was made at a simple ann

Q: A firm borrowed $1,500,000 from National Bank. The loan was made at a simple ann

a) approximate interest rate is: .09/(1-.20) = .1125 true effective rate = (1+(.1125/4))^4 = 11.73% b) Total interest = 1,500,000*.09*3/12 = $33,750 c) Net proceeds = gross loan-(compensating balance+interest) Net proceeds = 1,500,000-(300,000+33,750)= $1,166,250 Cost / net proceeds = 33,750/1,166,250 .02894 is for 3 months effective annual rate = 1.02894^4-1 = 1.1209 = .1209 = 12.09%

ID: 2627173 • Letter: A

Question

A firm borrowed $1,500,000 from National Bank. The loan was made at a simple annual interest rate of 9% a year for 3 months. A 20% compensating balance requirement raised the effective interest rate.

a) The nominal annual rate of the loan was 11.25%. What is the true effective rate?

b) What would be the effective cost of the loan if the note required discount interest?

c) What would be the nominal annual interest rate on the loan if the bank did not require a compensating balance but required repayment in 3 equal monthly installments?

Explanation / Answer

approximate interest rate is:

.09/(1-.20) = .1125

true effective rate = (1+(.1125/4))^4 = 11.73%

Total interest = 1,500,000*.09*3/12 = $33,750

Net proceeds = gross loan-(compensating balance+interest)

Net proceeds = 1,500,000-(300,000+33,750)= $1,166,250

Cost / net proceeds = 33,750/1,166,250

.02894 is for 3 months

effective annual rate = 1.02894^4-1 = 1.1209 = .1209 = 12.09%

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