Question 9
You want to buy a $\mathrm{\$}25,000\mathrm{car}$. The company is offering a $5\mathrm{\%}$ interest rate for 48 months (4 years). What will your monthly payments be?
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Check Answer

Step 1 ：We are given a car price of $25,000, an annual interest rate of 5%, and a loan term of 48 months. We want to find out the monthly payment.

Step 2 ：We can use the formula for calculating the monthly payment for a loan: $P=\frac{r\cdot PV}{1-(1+r{)}^{-n}}$, where P is the monthly payment, r is the monthly interest rate (annual rate / 12), PV is the present value (the amount of the loan), and n is the number of payments (months).

Step 3 ：First, we convert the annual interest rate to a monthly rate by dividing by 12. So, $r=\frac{5\mathrm{\%}}{12}=0.00416667$.

Step 4 ：Next, we substitute the given values into the formula: $P=\frac{0.00416667\cdot 25000}{1-(1+0.00416667{)}^{-48}}$.

Step 5 ：Solving the equation gives us the monthly payment, $P=575.73$.

Step 6 ：So, the monthly payment for the car will be approximately $575.73. Therefore, the final answer is $\boxed{{\displaystyle 575.73}}$.