terry has just purchased a new car, which had a list price of $16,825. she had to pay 7.19% sales tax, a…

terry has just purchased a new car, which had a list price of $16,825. she had to pay 7.19% sales tax, a $1,128 vehicle registration fee, and a $190 documentation fee. terry traded in her previous vehicle, a 2003 honda element in good condition to use as a down - payment. the dealer paid full price for her trade in. she financed the rest of the cost over five years at an interest rate of 10.59%, compounded monthly. what is her monthly payment? (round all dollar values to the nearest cent.)\n\nhonda cars in good condition\n|model/year|2000|2001|2002|2003|\n|----|----|----|----|----|\n|element|$5,887|$6,080|$6,225|$6,622|\n|odyssey|$8,450|$8,693|$8,928|$9,224|\n|insight|$4,384|$4,661|$5,006|$5,440|\n|accord|$6,356|$6,626|$6,817|$7,114|\n\na. $416.83\nb. $190.00\nc. $218.16\nd. $274.20

terry has just purchased a new car, which had a list price of $16,825. she had to pay 7.19% sales tax, a $1,128 vehicle registration fee, and a $190 documentation fee. terry traded in her previous vehicle, a 2003 honda element in good condition to use as a down - payment. the dealer paid full price for her trade in. she financed the rest of the cost over five years at an interest rate of 10.59%, compounded monthly. what is her monthly payment? (round all dollar values to the nearest cent.)\n\nhonda cars in good condition\n|model/year|2000|2001|2002|2003|\n|----|----|----|----|----|\n|element|$5,887|$6,080|$6,225|$6,622|\n|odyssey|$8,450|$8,693|$8,928|$9,224|\n|insight|$4,384|$4,661|$5,006|$5,440|\n|accord|$6,356|$6,626|$6,817|$7,114|\n\na. $416.83\nb. $190.00\nc. $218.16\nd. $274.20

Answer

Explanation:

Step1: Calculate the sales - tax amount

The sales - tax rate is $7.19%=0.0719$, and the list price of the car is $P = 16825$. The sales - tax amount $T$ is $T=0.0719\times16825=$1219.7275$.

Step2: Calculate the total cost of the car

The total cost $C$ of the car is the sum of the list price, sales - tax, vehicle registration fee, and documentation fee. The vehicle registration fee is $1128$ and the documentation fee is $190$. So $C = 16825+1219.7275 + 1128+190=$19362.7275$.

Step3: Determine the down - payment amount

Terry traded in a 2003 Honda Element. From the table, the value of a 2003 Honda Element in good condition is $6622$. So the down - payment $D = 6622$.

Step4: Calculate the loan amount

The loan amount $L$ is the total cost minus the down - payment. So $L=19362.7275 - 6622=$12740.7275$.

Step5: Calculate the monthly interest rate and number of payments

The annual interest rate $r = 10.59%=0.1059$. The monthly interest rate $i=\frac{0.1059}{12}=0.008825$. The number of payments $n = 5\times12 = 60$.

Step6: Use the loan - payment formula

The loan - payment formula is $M=\frac{L\times i\times(1 + i)^n}{(1 + i)^n-1}$. Substitute $L = 12740.7275$, $i = 0.008825$, and $n = 60$ into the formula. [ \begin{align*} (1 + i)^n&=(1 + 0.008825)^{60}\ &\approx1.71677\ M&=\frac{12740.7275\times0.008825\times1.71677}{1.71677 - 1}\ &=\frac{12740.7275\times0.008825\times1.71677}{0.71677}\ &=\frac{12740.7275\times0.015159}{0.71677}\ &=\frac{193.14}{0.71677}\ &\approx274.20 \end{align*} ]

Answer:

d. $$274.20$