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: i_eff = (1 + r/m)^m - 1.

Semiannual (m = 2):
i_semi = (1 + 0.08145/2)^2 - 1 = (1.040725)^2 - 1 = 0.0831085256 (8.31085256%)

Weekly (m = 52):
i_week = (1 + 0.08145/52)^52 - 1 ≈ 0.0847898107 (8.47898107%)

Difference = i_week - i_semi ≈ 0.0847898107 - 0.0831085256 ≈ 0.0016812851 = 0.16812851 percentage points ≈ 0.1681

Answer: c. 0.1681 percentage points.