Let's solve part (a) step by step: --- ### **Step 1: Adjust the Interest Rate to Monthly** - **Given:** - Nominal annual interest rate compounded semi-annually: **3.42%** - Monthly payments (12 per) First, convert the nominal rate to the effective monthly rate: - **Semi-annual rate:** \( \frac{3.42\%}{2} = 1.71\% \) - **Effective annual rate (EAR):** \( (1 + .0171)^2 - 1 = .03447441 \) or **3.4474%** - **Effective monthly rate:** \( (1 + \text{EAR})^{1/12} - 1 = (1.03447441)^{1/12} - 1 \approx .002825 \) or **.2825%** **Explanation:** The interest rate must match the payment frequency (monthly). We first convert to effective annual and then find the equivalent monthly rate. --- ### **Step 2: Use the Amortization Formula** - **Principal (\(P\))**: $43,200 - **Number of payments (\(n\))**: \(8 \times 12 = 96\) - **Monthly interest rate (\(i\))**: .002825 The payment formula is: \[ PMT = \frac{P \cdot i}{1 - (1 + i)^{-n}} \] Plug in the numbers: \[ PMT = \frac{43,200 \times .002825}{1 - (1 + .002825)^{-96}} \] \[ PMT = \frac{121.92}{1 - (1.002825)^{-96}} \] \[ (1.002825)^{96} \approx 1.3004 \implies (1.002825)^{-96} \approx .7687 \] \[ 1 - .7687 = .2313 \] \[ PMT = \frac{121.92}{.2313} \approx 527.16 \] Round up to the next whole number: **\$528** **Explanation:** We use the standard loan payment formula with the monthly rate and number of months. The answer is rounded up as requested. --- ## **Final Answer (Part a):** **The size of the monthly payment is \$528.**