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?