1. **Problem Statement:** Calculate the loan needed, monthly payment, and total cost for a Honda Odyssey priced at 25500 plus taxes, with a 3500 down payment, a 4-year loan at 4.5% interest. 2. **Formula and Rules:** - Loan amount = Selling price + taxes - down payment - Monthly payment for a loan with compound interest is given by the formula: $$M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$$ where $P$ is the principal (loan amount), $r$ is the monthly interest rate, and $n$ is the total number of payments (months). - Total cost = down payment + (monthly payment $\times$ number of months) 3. **Calculations:** - Assume taxes are not specified, so we calculate without taxes. - Loan needed: $P = 25500 - 3500 = 22000$ - Annual interest rate = 4.5%, so monthly rate $r = \frac{4.5}{100 \times 12} = 0.00375$ - Number of months $n = 4 \times 12 = 48$ 4. **Monthly payment:** $$M = 22000 \times \frac{0.00375(1+0.00375)^{48}}{(1+0.00375)^{48} - 1}$$ Calculate: - $(1+0.00375)^{48} = (1.00375)^{48} \approx 1.197$ (using compound interest approximation) - Numerator: $0.00375 \times 1.197 = 0.004489$ - Denominator: $1.197 - 1 = 0.197$ - Fraction: $\frac{0.004489}{0.197} \approx 0.02279$ - Monthly payment $M = 22000 \times 0.02279 = 501.38$ 5. **Total cost:** $$\text{Total cost} = 3500 + (501.38 \times 48) = 3500 + 24066.24 = 27566.24$$ **Final answers:** - a) Loan needed: $22000$ - b) Monthly payment: approximately $501.38$ - c) Total cost at end of loan: approximately $27566.24$