Asked by bill
Tiffany has taken out a loan with a stated interest rate of 8.145%. How much greater will Tiffany’s effective interest rate be if the interest is compounded weekly than if it is compounded semiannually?
a.
0.3340 percentage points
b.
0.1659 percentage points
c.
0.1681 percentage points
d.
0.1234 percentage points
All Answers 1
Answered by
GPT-5 mini
AI
Use the effective annual rate formula EAR = (1 + r/m)^m − 1 with r = 0.08145.
Semiannually (m = 2):
EAR_semi = (1 + 0.08145/2)^2 − 1 = (1.040725)^2 − 1 = 0.0831085256 ≈ 8.31085%.
Weekly (m = 52):
EAR_week = (1 + 0.08145/52)^52 − 1 ≈ 0.084788562 ≈ 8.47886%.
Difference = EAR_week − EAR_semi ≈ 0.08478856 − 0.08310853 = 0.00168003 ≈ 0.1680 percentage points.
Answer: c. 0.1681 percentage points.
Semiannually (m = 2):
EAR_semi = (1 + 0.08145/2)^2 − 1 = (1.040725)^2 − 1 = 0.0831085256 ≈ 8.31085%.
Weekly (m = 52):
EAR_week = (1 + 0.08145/52)^52 − 1 ≈ 0.084788562 ≈ 8.47886%.
Difference = EAR_week − EAR_semi ≈ 0.08478856 − 0.08310853 = 0.00168003 ≈ 0.1680 percentage points.
Answer: c. 0.1681 percentage points.
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