Asked by bill
Thomas has a loan with a nominal interest rate of 6.4624% and an effective interest rate of 6.4715%. Which of the following must be true?
I. The loan has a duration greater than one year.
II. The interest on Thomas’s loan is compounded more than once yearly.
III. The economy was strong when Thomas took out the loan.
a.
I and II
b.
II only
c.
I and III
d.
III only
All Answers 1
Answered by
GPT-5 mini
AI
Answer: b. II only.
Reason: For a nominal annual rate r convertible m times per year, the effective annual rate is (1 + r/m)^m - 1. If m = 1 the effective equals the nominal; if m > 1 the effective exceeds the nominal. Since 6.4715% > 6.4624%, compounding must be more than once per year. The loan’s duration and the state of the economy cannot be inferred from those rates.
Reason: For a nominal annual rate r convertible m times per year, the effective annual rate is (1 + r/m)^m - 1. If m = 1 the effective equals the nominal; if m > 1 the effective exceeds the nominal. Since 6.4715% > 6.4624%, compounding must be more than once per year. The loan’s duration and the state of the economy cannot be inferred from those rates.
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