1. **Problem Statement:** We have monthly payments of $341.82 for 2 years (24 months) with an annual interest rate of 11% compounded monthly. (a) Find the amount financed (present value of the payments). (b) Find the total interest cost. 2. **Formula and Explanation:** The amount financed is the present value of an annuity. The formula for the present value $PV$ of an annuity with payment $P$, interest rate per period $i$, and number of periods $n$ is: $$PV = P \times \frac{1 - (1 + i)^{-n}}{i}$$ Where: - $P = 341.82$ - Annual interest rate = 11%, so monthly interest rate $i = \frac{0.11}{12} = 0.0091667$ - Number of payments $n = 24$ 3. **Calculate the amount financed:** Calculate $i$: $$i = \frac{0.11}{12} = 0.0091667$$ Calculate the factor: $$1 - (1 + i)^{-n} = 1 - (1 + 0.0091667)^{-24} = 1 - (1.0091667)^{-24}$$ Calculate $(1.0091667)^{-24}$: $$ (1.0091667)^{24} = 1.244974 \Rightarrow (1.0091667)^{-24} = \frac{1}{1.244974} = 0.803441 $$ So the factor is: $$1 - 0.803441 = 0.196559$$ Now calculate present value: $$PV = 341.82 \times \frac{0.196559}{0.0091667} = 341.82 \times 21.4411 = 7327.99$$ 4. **Calculate the interest cost:** Total payments made: $$341.82 \times 24 = 8203.68$$ Interest cost: $$8203.68 - 7327.99 = 875.69$$ **Final answers:** (a) Amount financed = $7327.99$ (b) Interest cost = $875.69$