An installment contract for the purchase of a car requires payments of $\mathrm{\$}260.41$ at the end of each month for 2.25 years. Interest is $5\mathrm{\%}$ per annum compounded monthly.
(a) What is the amount financed?
(b) How much is the interest cost?
(a) The amount financed is $\mathrm{\$}$ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)
(b) The interest is $\mathrm{\$}◻$.
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Step 1 ：Given that the monthly payment (PMT) is $260.41, the annual interest rate (r) is 5% or 0.05, the number of compounding periods per year (n) is 12 (monthly), and the number of years (t) is 2.25.

Step 2 ：We can calculate the amount financed using the formula for the present value of an annuity: $PV=PMT\times \left[\frac{1-(1+\frac{r}{n}{)}^{-nt}}{\frac{r}{n}}\right]$.

Step 3 ：Substituting the given values into the formula, we get $PV=260.41\times \left[\frac{1-(1+\frac{0.05}{12}{)}^{-12\times 2.25}}{\frac{0.05}{12}}\right]$.

Step 4 ：Solving the equation, we find that the amount financed (PV) is approximately $6636.94.

Step 5 ：We can calculate the interest cost by subtracting the amount financed from the total payments made over the 2.25 years. The total payments made is $PMT\times n\times t=260.41\times 12\times 2.25$.

Step 6 ：Subtracting the amount financed from the total payments, we get the interest cost is approximately $394.13.

Step 7 ：Final Answer: (a) The amount financed is $\boxed{{\displaystyle \mathrm{\$}6636.94}}$. (b) The interest cost is $\boxed{{\displaystyle \mathrm{\$}394.13}}$.