Question

A firm has established a revolving line of credit for $900,000 with a bank at a rate of prime plus 2%. There is an annual fee of 1/2% on any unused funds. Interest is discounted on loans. Prime was 5% when the agreement was made. Assume the firm decides to take down the line for $500,000 for 60 days when the prime is at 6%. What is the effective annual rate?

Answer 1

Revolving line of credit = $900,000

Bank rate = Prime + 2%

Annual fee on unused funds = 0.5%

Prime at the time of agreement = 5%

Amount the firm decides to take down the line = $500,000

Tenure = 60 days

Prime at the time of taking down the line = 6%

Interest rate on the funds taken by the firm = Prime + 2% = 6% + 2% = 8%

Number of days (a)	Total Line of credit (b)	Amount taken by firm (c)	Interest rate on used funds (Prime + 2%) (d)	Interest on used funds (e) =(c)*(d)*(a)/360	Unused funds (f) = (b) – (c)	Interest on unused funds (g) = (f)*0.5% *(a)/360	Total Interest (f)=(e)+(g)
60	$900,000	$500,000	6% +2%= 8%	$6666.67	$400,000	$333.33	$7000
300	$900,000	NIL	Not Applicable	NIL	$900,000	$3750	$3750
				Total Interest			$10,750

Effective interest rate    = Interest accrued / Funds used or taken

                                           = $10750 / $500,000 for 60 days

                                           = 2.15% for 60 days

                                           = i.e., 2.15*360/60 = 12.9%

Therefore, 12.9% is the effective annual rate for the firm.