Juana is depositing a total of \( \$ 1000 \) in two accounts. - She will deposit \( \$ 600 \) into Account I, which earns \( 3.5 \% \) annual simple interest. - She will deposit \( \$ 400 \) into Account II, which earns \( 3.25 \% \) interest compounded annually. What is the total balance of these two accounts after 2 years?
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To calculate the total balance after 2 years, we first need to determine the balance in each account. **For Account I** (Simple Interest): - Principal (P) = $600 - Rate (R) = 3.5% = 0.035 - Time (T) = 2 years The formula for simple interest is: \[ \text{Interest} = P \times R \times T \] Calculating the interest: \[ \text{Interest} = 600 \times 0.035 \times 2 = 600 \times 0.07 = 42 \] So, the total balance in Account I after 2 years is: \[ \text{Total Balance in Account I} = P + \text{Interest} = 600 + 42 = 642 \] **For Account II** (Compound Interest): - Principal (P) = $400 - Rate (R) = 3.25% = 0.0325 - Time (T) = 2 years The formula for compound interest is: \[ A = P \times (1 + R)^T \] Calculating the total amount: \[ A = 400 \times (1 + 0.0325)^2 \] Calculating \( (1 + 0.0325)^2 \): \[ (1.0325)^2 \approx 1.0665 \] Now, calculate \( A \): \[ A = 400 \times 1.0665 \approx 426.60 \] Now, we’ll find the total balance of both accounts: \[ \text{Total Balance} = \text{Balance in Account I} + \text{Balance in Account II} = 642 + 426.60 = 1068.60 \] Therefore, the total balance of these two accounts after 2 years is approximately **$1068.60**.
