Which of the following one-year, $1,000 bank loans offers the lowest effective a
ID: 2617452 • Letter: W
Question
Which of the following one-year, $1,000 bank loans offers the lowest effective annual rate? a. A loan with an APR of 6.0%, compounded monthly. b. A loan with an APR of 6.0%, compounded annually, with a compensating balance requirement of 10.0% (on which no interest is paid). The EAR for the loan in this case is | |96. (Round to one decimal place.) b. A loan with an APR of 6.0%, compounded annually, with a compensating balance requirement of 10.0% (on which no interest is paid. The EAR for the loan in this case is 11%. (Round to one decimal place.) C. A loan with an APR of 6.0%, compounded annually, with a 1.00% loan origination fee. The EAR for the loan in this case is | |96. (Round to one decimal place.) Which bank loan offers the lowest effective annual rate? (Select the best choice below.) 0 A. The loan in part (c) is the cheapest. O B. The loan in part (b) is the cheapest ° C. The loan in part (a) is the cheapest. O D. The three loans are equivalent.Explanation / Answer
a). EAR = [1 + (APR / m) ^ m] - 1
= [{1 + (.06 / 12)} ^ 12 ] - 1 = .0617 X 100
= 6.17%
b). Compensating Balance = $1,000 x 0.10 = $100
Therefore, the borrower will have use of only $900(= $1,000 - $100)
Interest = $1,000 x 0.06 = $60
Hence, Interest Rate per period = $60/$900 = 6.67%
Since, this alternative assumes annual compounding, the effective annual rate is 6.67% as well.
C). The interest expense is $1,000×0.06 = $60
The loan origination fee is $1,000×0.01 = $10.
The loan origination fee reduces the usable proceeds of the loan to $990 because it is paid at the beginning of the loan.
The interest rate per period is $70/$990 = 7.07%.
Since the loan is compounded annually in this case, 7.07% is the effective annual rate.
4. Option "C" is correct, i.e., The loan in part (a) is the cheapest.
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