Question 9 You want to buy a $\$ 25,000 \mathrm{car}$. The company is offering a $5 \%$ interest rate for 48 months (4 years). What will your monthly payments be? $\$$ Check Answer
Solution
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, \(r = \frac{5\%}{12} = 0.00416667\).
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 \(\boxed{575.73}\).
