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.