Question

You’ve worked out a line of credit arrangement that allows you to borrow up to $40 million at any time. The interest rate is .44 percent per month. In addition, 4 percent of the amount that you borrow must be deposited in a noninterest-bearing account. Assume that your bank uses compound interest on its line of credit loans.

a. What is the effective annual interest rate on this lending arrangement? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

b. Suppose you need $14 million today and you repay it in 6 months. How much interest will you pay? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

a. What is the effective annual interest rate on this lending arrangement?

We have following information-

Borrowed amount A = $40 million

The amount deposited in a noninterest-bearing account = 4% of $40 million = $1.60 million

Therefore amount used = $40 million - $1.60 million = $38.40 million

But interest will be charged on borrowed amount

Therefore

Therefore interest I = A * (1+r) ^t – A

Where,

Borrowed amount A = $40 million

Interest amount I =?

Monthly interest rate r = 0.44%

Time period t = 1 months

Therefore

= $40 million * (1+ 0.44%) ^1 - $40 million

= $40.176 million - $40 million

= $0.176 million

But actual used amount is only $38.40 million

Therefore effective monthly interest rate on this lending arrangement

= ($0.176 million /$38.40 million) *100

= 0.4583% per month

The effective annual interest rate on this lending arrangement = (1+effective monthly rate) ^12 -1

= (1 + 0.4583%) ^12 -1

= 1.05641 -1 = 0.05641 or 5.64%

b. Suppose you need $14 million today and you repay it in 6 months. How much interest will you pay?

Assume that you have to borrow amount x from bank

Therefore,

x *(1-4%) = $14 million

Or x = $14 million / (1-4%) = $14.5833 million

So that you can use $14 million (96%) and $0.5833 million (4%) deposited in a noninterest-bearing account. But you have to pay interest on total amount of $14.5833 million

Therefore interest in six months I = A * (1+r) ^t – A

Where,

Borrowed amount A = $14.5833 million

Interest amount I =?

Monthly interest rate r = 0.44%

Time period t = 6 months

Therefore

= $14.5833 million * (1+ 0.44%) ^6 - $14.5833 million

= $14.9726 million -$14.5833 million

= $0.38926026 million or $ 389,260.26