jenna bought a new car for $31,000. she paid a 10% down - payment and financed the remaining balance for 60…

Explanation:

Step1: Calculate the loan amount

The car costs $31,000. The down - payment is 10% of $31,000. So the down - payment is $31,000\times0.1 = 3100$. The loan amount $P$ is $31000 - 3100=27900$.

Step2: Calculate the monthly interest rate

The annual percentage rate (APR) is 5.5%, so the monthly interest rate $r$ is $\frac{0.055}{12}$.

Step3: Calculate the number of payments

The loan is for 60 months, so $n = 60$.

Step4: Use the loan - payment formula

The formula for the monthly payment of a loan is $M=\frac{P\times r\times(1 + r)^n}{(1 + r)^n-1}$. Substitute $P = 27900$, $r=\frac{0.055}{12}$, and $n = 60$ into the formula. First, calculate $(1 + r)^n=(1+\frac{0.055}{12})^{60}$. Let $x=\frac{0.055}{12}\approx0.004583$. Then $(1 + 0.004583)^{60}\approx1.3199$. $P\times r=27900\times\frac{0.055}{12}\approx127.875$. $M=\frac{127.875\times1.3199}{1.3199 - 1}=\frac{127.875\times1.3199}{0.3199}$. $127.875\times1.3199 = 168.73$. $M=\frac{168.73}{0.3199}\approx527.45$.

Answer:

$527.45$