Questions: You want to buy a 25,000 car. You can make a 10% down payment, and will finance the balance with a 5% interest rate for 60 months (5 years). What will your monthly payments be?

You want to buy a 25,000 car. You can make a 10% down payment, and will finance the balance with a 5% interest rate for 60 months (5 years). What will your monthly payments be?

Transcript text: You want to buy a $25,000 car. You can make a $10\%$ down payment, and will finance the balance with a $5\%$ interest rate for 60 months (5 years). What will your monthly payments be?

Solution

Solution Steps

Step 1: Convert the Annual Interest Rate to a Monthly Interest Rate

To find the monthly interest rate, divide the annual interest rate by 12. Given an annual interest rate of 5%, the monthly interest rate is 0.00417 or 0.42%.

Step 2: Calculate the Monthly Payment

The formula to calculate the monthly payment is: \[M = P \frac{r(1+r)^n}{(1+r)^n - 1}\] Substitute the values into the formula: \[M = 22500 \times \frac{0.00417(1+0.00417)^60}{(1+0.00417)^60 - 1}\] After calculation, the monthly payment is approximately 424.6.