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.