Question

aufqr2 4.6.001.
a computer chip designer purchased a car for $52,876.47, which included sales tax and registration. if the designer obtains a 5-year loan for the total amount at an annual interest rate of 5.1% compounded monthly, find the monthly car payment. (round your answer to the nearest cent.)
$

Explanation:

Step1: Define variables

Let $P = 52876.47$ (loan principal), $r = 0.051$ (annual rate), $n = 12$ (monthly compounding), $t = 5$ (loan term in years).

Step2: Calculate monthly rate

$i = \frac{r}{n} = \frac{0.051}{12} = 0.00425$

Step3: Calculate total number of payments

$N = n \times t = 12 \times 5 = 60$

Step4: Apply monthly payment formula

Monthly payment $M = P \times \frac{i(1+i)^N}{(1+i)^N - 1}$
Substitute values:
$M = 52876.47 \times \frac{0.00425(1+0.00425)^{60}}{(1+0.00425)^{60} - 1}$
First compute $(1.00425)^{60} \approx 1.28303$
Then:
$M = 52876.47 \times \frac{0.00425 \times 1.28303}{1.28303 - 1}$
$M = 52876.47 \times \frac{0.0054528775}{0.28303}$
$M = 52876.47 \times 0.019265$

Step5: Compute final payment

$M \approx 1018.60$

Answer:

$\$1018.60$