Question

You've worked out a line of credit arrangement that allows you to borrow up to $70 million at any time. The interest rate is 0.61 percent per month. In addition, 2 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)8.04%10.46%7.60%7.73%7.57%

  

(b)	Suppose you need $16 million today and you repay it in 7 months. How much interest will you pay? (Do not round your intermediate calculations.)
	(Click to select)-15,836,634.69695,830.4516,930,266.221,036,561.68710,031.07

Answer 1

Sol:

Borrowing limit = $70 million

Interest rate (r) = 0.61% per month

Amount to be deposited in a non-interest-bearing account = 2%

Period9n) = 12 months

a) to compute effective annual interest rate

Effective annual interest rate = (1 + r)^n - 1 / (1 - non-interest-bearing cost)

Effective annual interest rate = (1 +0.61%)^12 - 1 / (1 - 2%)

Effective annual interest rate = (1.0061)^12 - 1 / (1 - 0.02)

Effective annual interest rate = 0.0757 / 0.98 = 0.07725 or 7.73%

b)

Present value (PV) = $16 million

Period (n) = 7 months

To compute interest you will pay:

Borrowed amount = PV / (1 - 2%)

Borrowed amount = 16,000,000 / (1 - 0.02)

Borrowed amount = $16,326,530.61

Interest to pay = Borrowed amount * (1 + r)^n - Borrowed amount

Interest to pay = 16,326,530.61 * (1 + 0.61%)^7 - 16,326,530.61

Interest to pay = (16,326,530.61 * 1.0435) - 16,326,530.61

Interest to pay = 17,036,561.68 - 16,326,530.61 = $710,031.07

Therefore interest amount you will pay will be $710,031.07