Let’s break it down step by step: ### 1. **Vehicle Price and Down Payment** - **Vehicle price:** $25,000 - **Down payment:** $7,000 - **Amount to finance (loan amount):** \[ \$25,000 - \$7,000 = \$18,000 \] ### 2. **Loan Details** - **Loan amount:** $18,000 - **Term:** 3 years (36 months) - **Annual interest rate:** 2% - **Monthly interest rate:** \[ \frac{2\%}{12} = \frac{0.02}{12} = 0.0016667 \] ### 3. **Monthly Payment Formula** The formula for a fixed-rate loan monthly payment (\(M\)) is: \[ M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \] Where: - \(P\) = loan amount ($18,000) - \(r\) = monthly interest rate (0.0016667) - \(n\) = total number of payments (36) ### 4. **Plug in the numbers** #### **Step 1: Calculate \((1 + r)^n\)** \[ (1 + 0.0016667)^{36} = (1.0016667)^{36} \] Let’s calculate that part: \[ (1.0016667)^{36} \approx 1.0616778 \] #### **Step 2: Plug into the formula** \[ M = \frac{18000 \times 0.0016667 \times 1.0616778}{1.0616778 - 1} \] \[ M = \frac{18000 \times 0.0016667 \times 1.0616778}{0.0616778} \] #### **Step 3: Calculate the numerator** \[ 18000 \times 0.0016667 = 30 \] \[ 30 \times 1.0616778 = 31.850334 \] #### **Step 4: Final calculation** \[ M = \frac{31.850334}{0.0616778} \approx 516.47 \] --- ## **Final Answer:** **Your monthly payment would be:** \[ \boxed{516.47} \] **(Rounded to two decimal places, units: dollars)** --- ### **Summary Table** | Step | Value | |------------------------------------|---------------:| | Vehicle Price | $25,000 | | Down Payment | $7,000 | | Loan Amount | $18,000 | | Interest Rate (annual) | 2% | | Loan Term (months) | 36 | | Monthly Payment | $516.47 |

Certainly! Here's a one-line explanation for each step: 1. Subtract the down payment from the vehicle price to find the amount to finance. 2. Note the loan duration in months and the annual interest rate. 3. Convert the annual interest rate into a monthly interest rate. 4. Use the loan payment formula with these values to calculate the monthly payments. 5. Calculate \((1 + r)^n\) to account for interest compounding over the loan period. 6. Plug all values into the formula and compute to find the monthly payment.