Question

Melanie is looking for a loan. She is willing to pay no more than an effective rate of 9.955% annually. Which, if any, of the following loans meet Melanie’s criteria?

Loan A: 9.265% nominal rate, compounded weekly
Loan B: 9.442% nominal rate, compounded monthly
Loan C: 9.719% nominal rate, compounded quarterly
a.
B only
b.
A and C
c.
A and B
d.
None of these fit Melanie’s criteria.

Answer 1

The correct answer is C.

Explanation:

Giving the following information:

Loan A: 9.265% nominal rate, compounded weekly

Loan B: 9.442% nominal rate, compounded monthly

Loan C: 9.719% nominal rate, compounded quarterly

To calculate the effective annual rate, we need to use the following formula:

Effective annual rate= [(1+i)^n] - 1

Loan A:

i= 0.09265/52= 0.001782

Effective annual rate= [(1.001782^52) - 1]

Effective annual rate= 0.097 = 9.7%

Loan B:

i= 0.09442/12= 0.007868

Effective annual rate= [(1.007868^12) - 1]

Effective annual rate= 0.0986 = 9.86%

Loan C:

i= 0.09719/4= 0.02439

Effective annual rate= [(1.02439^4) - 1]

Effective annual rate= 10.11%