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Homework answers / question archive / ou've worked out a line of credit arrangement that allows you to borrow up to $45 million at any time
ou've worked out a line of credit arrangement that allows you to borrow up to $45 million at any time. The interest rate is .41 percent per month. In addition, 4 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.
a.What is the effective annual interest rate on this lending arrangement? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b.Suppose you need $11 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.)
a) Computation of Effective Annual Interest Rate on this lending arrangement:
Given,
Borrowed amount (A) = $45 million
Amount deposited in a noninterest-bearing account = 4% of $45 million = $1.80 million
Amount Used = $45 million - $1.80 million = $43.20 million
But interest will be charged on borrowed amount
So,
Interest = A * (1+r) ^t - A
Here,
Monthly interest rate (r) = 0.41%
Time period (t) = 1 months
Interest = $45 million * (1+ 0.41%) ^1 - $45 million
= $45.1845 million - $45 million
Interest = $0.1845 million
But actual used amount is only $43.20 million
Therefore,
Effective Monthly Interest Rate on this lending arrangement = ($0.1845 million /$43.20 million) *100 = 0.4271% per month
Effective Annual Interest Rate on this lending arrangement = (1+Effective Monthly Rate) ^12 -1
= (1 + 0.4271%) ^12 -1
= 1.05247 -1 = 0.05247 or 5.25%
b) Computation of Interest:
Assume that you have to borrow amount x from bank
Therefore,
x *(1-4%) = $11 million
Or
x = $11 million / (1-4%) = $11.4583 million
So that you can use $11 million (96%) and $0.4583 million (4%) deposited in a noninterest-bearing account. But you have to pay interest on total amount of $11.4583 million
Therefore,
Interest in six months I = A * (1+r) ^t - A
Here,
Borrowed amount A = $11.4583 million
Interest amount I =?
Monthly interest rate r = 0.41%
Time period t = 6 months
Interest = $11.4583 million * (1+ 0.41%) ^6 - $11.4583 million
= $11.7431 million -$11.4583 million
Interest = $0.2847806 million or $284,780.06
