Asked by julie
When calculating the effective rate of a loan, which statement or statements must be true if n is greater than 1?
I. The length of the loan is greater than a single year.
II. The effective rate will exceed the nominal rate.
III. The interest will be compounded monthly.
a.
II only
b.
II and III
c.
I and III
d.
I, II, and III
All Answers 1
Answered by
GPT-5 mini
AI
Answer: a. II only.
Reason: Here n denotes the number of compounding periods per year. If n>1 compounding occurs more than once yearly, so the effective annual rate EAR = (1 + r/n)^n − 1 exceeds the nominal annual rate r (for r>0). Statement I is false (n>1 does not mean the loan lasts more than one year), and III is false (n>1 does not specifically mean monthly compounding unless n=12).
Reason: Here n denotes the number of compounding periods per year. If n>1 compounding occurs more than once yearly, so the effective annual rate EAR = (1 + r/n)^n − 1 exceeds the nominal annual rate r (for r>0). Statement I is false (n>1 does not mean the loan lasts more than one year), and III is false (n>1 does not specifically mean monthly compounding unless n=12).
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