1. The problem asks which account has the highest annual interest rate considering different compounding frequencies and nominal rates. 2. The formula to find the effective annual rate (EAR) when interest is compounded $n$ times per year at a nominal rate $r$ is: $$EAR = \left(1 + \frac{r}{n}\right)^n - 1$$ 3. We will calculate the EAR for each account: - Account 1: compounded annually ($n=1$), $r=0.0328$ $$EAR_1 = \left(1 + \frac{0.0328}{1}\right)^1 - 1 = 0.0328 = 3.28\%$$ - Account 2: compounded monthly ($n=12$), $r=0.0325$ $$EAR_2 = \left(1 + \frac{0.0325}{12}\right)^{12} - 1$$ Calculate: $$EAR_2 = (1 + 0.0027083)^{12} - 1 \approx 1.0330 - 1 = 0.0330 = 3.30\%$$ - Account 3: compounded weekly ($n=52$), $r=0.0310$ $$EAR_3 = \left(1 + \frac{0.0310}{52}\right)^{52} - 1$$ Calculate: $$EAR_3 = (1 + 0.00059615)^{52} - 1 \approx 1.0315 - 1 = 0.0315 = 3.15\%$$ - Account 4: compounded daily ($n=365$), $r=0.0315$ $$EAR_4 = \left(1 + \frac{0.0315}{365}\right)^{365} - 1$$ Calculate: $$EAR_4 = (1 + 0.0000863)^{365} - 1 \approx 1.0320 - 1 = 0.0320 = 3.20\%$$ - Account 5: compounded quarterly ($n=4$), $r=0.0325$ $$EAR_5 = \left(1 + \frac{0.0325}{4}\right)^4 - 1$$ Calculate: $$EAR_5 = (1 + 0.008125)^4 - 1 \approx 1.0330 - 1 = 0.0330 = 3.30\%$$ 4. Comparing the EARs: - Account 1: 3.28% - Account 2: 3.30% - Account 3: 3.15% - Account 4: 3.20% - Account 5: 3.30% 5. Accounts 2 and 5 have the highest effective annual rate of approximately 3.30%. 6. Since both have the same EAR, either Account 2 or Account 5 can be considered the highest. Final answer: Account 2 and Account 5 have the highest annual interest rate at approximately 3.30%.