Question

**You’ve worked out a line of credit arrangement that
allows you to borrow up to $10,000 at any time. The interest rate
is 0.75% per month. In addition, 2% of the amount that you borrow
must be deposited in a noninterest-bearing account.**

**a) What is the Effective Annual Rate on this lending
arrangement?**

**b) Suppose you need $8,000 today and you repay it in 9
months. How much interest**

**will you pay?**

Answer #1

a)

The EAR of the loan without the compensating balance is:

EAR = (1 + 0.0075)^{12}– 1

EAR = 0.093807 or 9.3807%

However, with the compensating balance, you will only get the use of part of the amount, so the EAR with the compensating balance will be:

EAR = 0.093807 / (1 – 0.02)

EAR = 0.09572132 or 9.57%

(b)

To end up with $8,000, you must borrow:

Amount to borrow = $8,000 / (1 – 0.02)

Amount to borrow = $8,163.26

The total interest you will pay on the loan is:

Total interest paid = $8163.26 (1.0075)^{9} –
8163.26

Total interest paid = $567.84

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