Question

Yunes’ Yearlings (YY) is able to raise funds by issuing commercial paper with a face value of $100,000. If commercial paper is issued, the simple interest rate would be 5 percent, the time to maturity would be 90 days, and YY would have to pay a transaction fee equal to 0.25 percent of the issue, which would be taken out of the issue amount. Compute the commercial paper’s APR and rEAR.

Answer 1

Annual percentage rate (APR)
An annual percentage rate (APR) is the annual rate charged for borrowing or earned through an investment, and is expressed as a percentage that represents the actual yearly cost of funds over the term of a loan. This includes any fees or additional costs associated with the transaction but does not take compounding into account.
Face value	=	$100,000
Transaction fee	=	0.25% on face value
	=	$250.00
Interest rate is	=	5%
Interest amount	=	net face value * 5%*90/360
Assume no of days as 360 in a year
	=	($100,000+$250)*5%*0.25
	=	1,253
Annual percentage rate	=	1,253/100,000
	=	1%
		1%*360/90
	=	4%
Annual percentage rate is 4%
b)
Effective annual rate
Par value		$100,000
interest rate		5%
fee		0.25%
maturity		90	days
Funds received	=	100,000-(100,00*0.25%)-(100,000*5%)*90/360
	=	98,500
Interest charge	=	100,000*5%*90/360
	=	1250
Transaction fee	=	100,000*0.25%
	=	250
Effective annual rate	=	(interest+transaction fee/Funds received)*360/90
	=	((1,250+250)/98500)*360/90
	=	0.01522*4
	=	6%
Effecrive annual rate is 6%