Subjects finance

Car Finance C33032

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Car Finance C33032


1. **Problem statement:** Calculate the amount financed and the interest cost for a car purchase with monthly payments of 341.82 for 2 years, at 11% annual interest compounded monthly. 2. **Formula used:** The amount financed is the present value (PV) of an annuity: $$PV = P \times \frac{1 - (1 + i)^{-n}}{i}$$ where: - $P = 341.82$ (monthly payment) - $i = \frac{0.11}{12} = 0.009167$ (monthly interest rate) - $n = 2 \times 12 = 24$ (total number of payments) 3. **Calculate the present value:** Calculate $1 + i = 1 + 0.009167 = 1.009167$ Calculate $(1 + i)^{-n} = 1.009167^{-24} \approx 0.800737$ Calculate numerator: $1 - 0.800737 = 0.199263$ Calculate denominator: $i = 0.009167$ Calculate fraction: $\frac{0.199263}{0.009167} \approx 21.7311$ Calculate present value: $PV = 341.82 \times 21.7311 = 7425.68$ 4. **Interpretation:** The amount financed (present value) is approximately 7425.68. 5. **Calculate interest cost:** Total payments = $341.82 \times 24 = 8203.68$ Interest cost = Total payments - Amount financed = $8203.68 - 7425.68 = 778.00$ 6. **Final answers:** (a) Amount financed = 7425.68 (b) Interest cost = 778.00 All intermediate values rounded to six decimal places as needed.