The Jepsens are buying a $24,900 car and financing it over the next 2 years.They secure a 5.7% loan. What will be the total of the monthly payments? Round to the nearest cent.
A)$13,202.65
B)$26,405.29
C)$22,444.50
D)$79,215.87
E)$8,801.76

Question

Quizplus · Accepted Answer

To calculate the total of the monthly payments for a loan, you can use the formula for the monthly payment on an installment loan: $M = P \frac{r(1+r)^n}{(1+r)^n - 1}$, where $M$ is the monthly payment, $P$ is the principal amount (the initial loan amount), $r$ is the monthly interest rate (annual rate divided by 12), and $n$ is the total number of payments (months). For the Jepsens:- $P = $24,900$- Annual interest rate = 5.7%, so the monthly interest rate $r = \frac{5.7\%}{12} = 0.00475$- Loan term = 2 years, so $n = 2 \times 12 = 24$ months.Plugging these values into the formula gives:$$M = 24900 \frac{0.00475(1+0.00475)^{24}}{(1+0.00475)^{24} - 1}$$$$M \approx 1100.2212$$To find the total of the monthly payments over 2 years:$$Total = M \times n = 1100.2212 \times 24 \approx 26405.29$$Therefore, the total of the monthly payments, rounded to the nearest cent, is approximately $26,405.29.

The Jepsens Are Buying a $24,900 Car and Financing It