Asked by damon
Say you are considering two loans. Loan F has a nominal interest rate of 5.66%, compounded monthly. Loan G has a rate of 6.02%, compounded semiannually. Which loan will give the lower effective interest rate, and how much lower will it be?
a.
Loan G’s effective rate will be 0.091 percentage points lower than Loan F’s.
b.
Loan G’s effective rate will be 0.058 percentage points lower than Loan F’s.
c.
Loan F’s effective rate will be 0.302 percentage points lower than Loan G’s.
d.
Loan F’s effective rate will be 0.149 percentage points lower than Loan G’s.
All Answers 1
Answered by
GPT-5 mini
AI
Compute the effective annual rates.
Loan F (5.66% nominal, monthly):
i_F = (1 + 0.0566/12)^{12} − 1 = (1 + 0.0047166667)^{12} − 1 ≈ 0.058094 ≈ 5.8094%
Loan G (6.02% nominal, semiannual):
i_G = (1 + 0.0602/2)^{2} − 1 = (1 + 0.0301)^{2} − 1 = 0.06110601 ≈ 6.1106%
Difference: i_G − i_F ≈ 0.061106 − 0.058094 = 0.003012 ≈ 0.3012 percentage points ≈ 0.302%.
So Loan F has the lower effective rate, about 0.302 percentage points lower than Loan G — answer (c).
Loan F (5.66% nominal, monthly):
i_F = (1 + 0.0566/12)^{12} − 1 = (1 + 0.0047166667)^{12} − 1 ≈ 0.058094 ≈ 5.8094%
Loan G (6.02% nominal, semiannual):
i_G = (1 + 0.0602/2)^{2} − 1 = (1 + 0.0301)^{2} − 1 = 0.06110601 ≈ 6.1106%
Difference: i_G − i_F ≈ 0.061106 − 0.058094 = 0.003012 ≈ 0.3012 percentage points ≈ 0.302%.
So Loan F has the lower effective rate, about 0.302 percentage points lower than Loan G — answer (c).
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