# A 477698 plus or minus 1000 compute and compare 3

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A. \$4,776.98 (plus or minus \$10.00) Compute and compare 3 loan EARs 7. Bianca is deciding among 3 loans that would each involve her receiving \$8,000 today and then paying back the original principal and all accrued interest in 1 year from today. Loan A has an APR of 14.40%, compounded annually. Loan B has an APR of 13.60%, compounded quarterly. Loan C has an APR of 13.60%, compounded continuously. Which of the following assertions is true if Bianca prefers loans with lower costs more than she prefers loans with higher costs? C. Bianca would prefer loan B to loan A and Bianca would prefer loan A to loan C
To answer this question, find and compare the EARs of the loans. Loans with lower EAR have lower costs, all else equal, because EAR reflects the true cost of a loan. Therefore, a loan with a lower EAR would be preferred to a comparable loan with a higher EAR. When compounding is not continuous: EAR = [(1 + periodic rate) # of periods in a year ] – 1 = [(1 + (APR/# periods in a year)) # of periods in a year ] – 1 When compounding is continuous: EAR = e APR – 1 EAR(A) = [(1 + (.1440 / 1)) 1 ] – 1 = [(1 + .1440) 1 ] – 1 = [(1.1440) 1 ] – 1 = .1440 = 14.40% EAR(B) = [(1 + (.1360 / 4)) 4 ] – 1 = [(1 + .0340) 4 ] – 1 = [(1.0340) 4 ] – 1 = .1431 = 14.31% EAR(C) = e .1360 – 1 = 1.1457 – 1 = .1457 = 14.57% Since EAR(A) > EAR(B), Bianca would prefer loan B to loan A Since EAR(C) > EAR(A), Bianca would prefer loan A to loan C Answer: C. Bianca would prefer loan B to loan A and Bianca would prefer loan A to loan C 7. Bianca is deciding among 3 loans that would each involve her receiving \$8,000 today and then paying back the original principal and all accrued interest in 1 year from today. Loan A has an APR of 15.50%, compounded annually. Loan B has an APR of 14.80%, compounded quarterly. Loan C has an APR of 14.80%, compounded continuously. Which of the following assertions is true if Bianca prefers loans with lower costs more than she prefers loans with higher costs? A. Bianca would prefer loan A to loan B and Bianca would prefer loan A to loan C 7. Bianca is deciding among 3 loans that would each involve her receiving \$8,000 today and then paying back the original principal and all accrued interest in 1 year from today. Loan A has an APR of 15.30%, compounded annually. Loan B has an APR of 14.40%, compounded continuously. Loan C has an APR of 14.40%, compounded quarterly. Which of the following assertions is true if Bianca prefers loans with lower costs more than she prefers loans with higher costs? B. Bianca would prefer loan A to loan B and Bianca would prefer loan C to loan A 7. Bianca is deciding among 3 loans that would each involve her receiving \$8,000 today and then paying back the original principal and all accrued interest in 1 year from today. Loan A has an APR of 16.40%, compounded annually. Loan B has an APR of 15.60%, compounded continuously. Loan C has an APR of 15.60%, compounded quarterly. Which of the following assertions is true if Bianca prefers loans with lower costs more than she prefers loans with higher costs?
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