1. **State the problem:** Puk wants to decide between two savings accounts with different interest rates and compounding frequencies to maximize her savings. 2. **Formula used:** The effective annual rate (EAR) is used to compare different compounding options. The formula for EAR is: $$EAR = \left(1 + \frac{r}{n}\right)^n - 1$$ where $r$ is the nominal annual interest rate (as a decimal), and $n$ is the number of compounding periods per year. 3. **Calculate EAR for Bank Forever:** - Interest rate $r = 2.18\% = 0.0218$ - Compounding monthly means $n = 12$ $$EAR = \left(1 + \frac{0.0218}{12}\right)^{12} - 1 = \left(1 + 0.0018167\right)^{12} - 1$$ Calculate: $$EAR = (1.0018167)^{12} - 1 \approx 1.0220 - 1 = 0.0220 = 2.20\%$$ 4. **Calculate EAR for Bank of Savings:** - Interest rate $r = 2.22\% = 0.0222$ - Compounding semiannually means $n = 2$ $$EAR = \left(1 + \frac{0.0222}{2}\right)^2 - 1 = \left(1 + 0.0111\right)^2 - 1$$ Calculate: $$EAR = (1.0111)^2 - 1 = 1.0223 - 1 = 0.0223 = 2.23\%$$ 5. **Compare EARs:** - Bank Forever EAR = 2.20\% - Bank of Savings EAR = 2.23\% 6. **Conclusion:** Since Bank of Savings offers a slightly higher effective annual rate, Puk should choose the Bank of Savings account to maximize her savings.