Question

Renee is going to buy a new car that has a list price of $19,675. She will be responsible for $1,420 in vehicle registration fees, $85 in documentation fees, and 8. 92% sales tax. She plans to trade in her current car, a 2002 Buick LeSabre in good condition, and finance the rest of the cost over four years at an interest rate of 11. 34%, compounded monthly. If the dealer gives Renee 85% of the listed trade-in value for her car, what will her monthly payment be? Round all dollar values to the nearest cent. Buick Cars in Good Condition Model/Year 1998 1999 2000 2001 2002 Century $929 $1,086 $1,150 $1,488 $1,595 LeSabre $2,075 $2,282 $2,690 $2,935 $3,374 Regal $1,676 $1,794 $2,030 $2,214 $2,566 Riviera $1,291 $1,455 $1,520 $1,814 $1,959 a. $521. 96 b. $508. 80 c. $518. 80 d. $504. 46.

Answer 1

The correct statement is that the monthly payments on the purchase of a new car by Renee will be $655 on the  interest rate of 11.34 percent for a period of four years.

The calculation of the value of the monthly payments to be made by Renee can be ascertained by computing all the costs of such transaction and then division by the number of months available.

Calculation of Monthly Payments

The total principal net value of the car comes down to $19945 after adding all the costs and deducting the trade-in value of the old car at 85% of the total value.

The formula for the calculation of total annuity is as below and the values given are being applied,

$\rm Compounded\ Annuity= P(1+ \dfrac{r}{n})^n^t\\\\\rm Compounded\ Annuity=19945(1+0.00945)^4^8\\\\\rm Compounded\ Annuity= \ 31450$

Now the monthly payments over a period of four years will be,

$\rm Monthly\ Payments = \dfrac{Annuity}{No. \ of\ Months}\\\\\rm Monthly\ Payments = \dfrac{31450}{48}\\\\\rm Monthly\ Payments = \ 655$

So, a monthly payment of $655 needs to be made in order to purchase such a car.

Hence, the correct statement is that the monthly payments on the purchase of a new car by Renee will be $655 on the  interest rate of 11.34 percent for a period of four years.

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