Bank A offers loans with a 10% state annual rate and a 10% compensating balance.

Question

Bank A offers loans with a 10% state annual rate and a 10% compensating balance. You wish to obtain $250,000 in a 6 month loan. a. How much must you borrow in order to obtain $250,000 in usable funds? Assume you currently do not have any funds on deposit at the bank. What is the effective annual rate on a 6 month loan? b. How much must you borrow to obtain $250,000 in usable funds if you currently have $10,000 on deposit at the bank? What is the effective annual rate on a 6 month loan? c. How much must you borrow to obtain $250,000 in usable funds if you currently have $30,000 on deposit at the bank? d. What is the effective annual rate on a 6 month loan?

Explanation / Answer

10% compensating balance -> need 10% of the loan deposited in the bank as collateral

a) EAR on 6-month loan   = (1+0.1/2)2-1 = 10.25%

b) for $250,000 usable fund we need to borrow

$250,000/(1-0.1) = $277,777.78

Since you already have $10,000 in the bank, you need to borrow $277,777.78-$10,000 = $267,777.78

You have to pay for interest = $267,777.78*10%/2 = $13,388.89

Implied interest rate =  $13,388.89/$250,000 = 5.356% (on 6 month)

EAR on 6-month loan = (1+0.05356)2-1 = 11%

c)

Since you already have $30,000 in the bank, you need to borrow $277,777.78-$30,000 = $247,777.78

d)

You have to pay for interest = $247,777.78*10%/2 = $12,388.89

Implied interest rate = $12,388.89/$250,000 = 4.956% (on 6 month)

EAR on 6-month loan = (1+0.04956)2-1 = 10.16%

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