Which bank should Ella choose for her investment based on the total amount of interest accrued over 2 years?

Answer

To determine which bank Ella should choose based on the total interest earned over 2 years, we will calculate the compound interest for both Northway Bank and Portland Bank using the formula for compound interest: \[ A = P(1 + r)^n \] where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial amount of money). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of years the money is invested for. ### For Northway Bank: - Principal (\( P \)) = €6000 - Annual interest rate (\( r \)) = 3.8% = 0.038 - Number of years (\( n \)) = 2 1. **Calculate the total amount using compound interest formula:** \[ A = 6000(1 + 0.038)^2 \] \[ A = 6000(1.038)^2 \] \[ A = 6000(1.077444) \] \[ A \approx 6464.67 \] 2. **Calculate total interest earned:** Total interest = Total amount - Principal = \( A - P \) \[ Total Interest = 6464.67 - 6000 \] \[ Total Interest \approx 464.67 \] ### For Portland Bank: - Principal (\( P \)) = €6000 - Year 1 interest rate (\( r_1 \)) = 5% = 0.05 - Year 2 interest rate (\( r_2 \)) = 3.2% = 0.032 1. **Calculate the amount after year 1:** \[ A_1 = 6000(1 + 0.05) \] \[ A_1 = 6000(1.05) \] \[ A_1 = 6300 \] 2. **Calculate the amount after year 2:** \[ A_2 = 6300(1 + 0.032) \] \[ A_2 = 6300(1.032) \] \[ A_2 \approx 6501.60 \] 3. **Calculate total interest earned:** Total interest = Total amount after 2 years - Principal = \( A_2 - P \) \[ Total Interest = 6501.60 - 6000 \] \[ Total Interest \approx 501.60 \] ### Conclusion: - Interest earned from Northway Bank: \( €464.67 \) - Interest earned from Portland Bank: \( €501.60 \) Since the total interest from Portland Bank is greater, Ella should choose **Portland Bank**.