Question

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a logo design company purchases four new computers for $18,500. the company finances the cost of the computers for 3 years at an annual interest rate of 6.125% compounded monthly. find the monthly payment (in dollars) for this loan. (round your answer to the nearest cent. see example 8 in this section.)
$

Explanation:

Step1: Define variables

Let $P = 18500$ (principal loan amount), $r = 0.06125$ (annual interest rate), $n = 12$ (compounding periods per year), $t = 3$ (loan term in years).

Step2: Calculate monthly rate & total periods

Monthly rate: $i = \frac{r}{n} = \frac{0.06125}{12}$
Total periods: $N = n \times t = 12 \times 3 = 36$

Step3: Use loan payment formula

The monthly payment formula is $M = P \times \frac{i(1+i)^N}{(1+i)^N - 1}$
Substitute values:
First calculate $i = \frac{0.06125}{12} \approx 0.00510417$
$(1+i)^N = (1+0.00510417)^{36} \approx 1.1997$
Then:
$M = 18500 \times \frac{0.00510417 \times 1.1997}{1.1997 - 1}$

Step4: Compute numerator & denominator

Numerator: $0.00510417 \times 1.1997 \approx 0.006123$
Denominator: $1.1997 - 1 = 0.1997$

Step5: Final calculation

$M = 18500 \times \frac{0.006123}{0.1997} \approx 18500 \times 0.03066 \approx 567.21$

Answer:

$\$567.21$