Question

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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

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.