To calculate the total amount Rachel will pay to pay off the purchase with monthly payments of $60, we need to first calculate the total number of months it will take to pay off the purchase.
Let X be the total number of months
Payment per month = $60
Total purchase price = $1400
APR = 18.11%
Using the formula for monthly payment on a credit card:
Payment per month = [Monthly APR * Total purchase price] / [1 - (1 + Monthly APR)^(-X)]
$60 = [0.1811/12 * $1400] / [1 - (1 + 0.1811/12)^(-X)]
$60 = [0.0150916667 * $1400] / [1 - (1.0150916667)^(-X)]
$60 = $21.125 / (1 - 1.0150916667)^(-X)
$60 = $21.125 / (1 - (1 / 1.0150916667)^X)
$60 = $21.125 / (1 - 0.98499375932087^X)
Then, solve for X by rearranging the formula:
(1 - 0.98499375932087^X) = $21.125 / $60
0.98499375932087^X = 1 - $21.125 / $60
0.98499375932087^X = 0.6454166667
X = ln(0.6454166667) / ln(0.98499375932087)
X = 40.2019621
Since the number of payments should be rounded up to the nearest whole number, Rachel will make 41 payments.
Total amount Rachel will pay = 41 payments * $60 = $2460
Therefore, Rachel will pay a total of $2460 to pay off the purchase with monthly payments of $60.
Rachel is purchasing a new camera that costs $1400. Rachel uses a credit card that has an APR of 18.11 % . How much will she pay in total to pay off the purchase if she makes monthly payments of $60? Round the number of monthly payments up to the nearest whole number. Round your final answer to the nearest whole number, if necessary.
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