You’ve worked out a line of credit arrangement that allows you to borrow up to $
ID: 2616703 • Letter: Y
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.)
Explanation / Answer
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
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.