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- anonymous

Can someone help me with this question? Anyone know the formula to use?
Aubrey uses her credit card to buy some clothes for $552.86. She can pay up to $195 on the credit card each month. What is the total cost of her purchase if the APR on the credit card is 27.3% compounded monthly?

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- anonymous

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- anonymous

Annual Percentage Rate (APR)
If a yearly interest rate i is compounded q times per year, where q is greater than 1, this will be equivalent to a higher rate, r, of simple interest paid at the end of the year. The latter rate is called the annual percentage rate (APR). It is given by the formula
r = (1+[i/q])q-1.
To find the interest rate i given the APR r, use
i = q[(1+r)1/q-1].
The APR is mainly used to compare loans with different interest rates and payment intervals. The lower the APR, the lower the cost of the loan to the borrower.
Example: Suppose your credit card charges 18% interest per year, but you have to pay the interest due monthly. What is the annual percentage rate? Here the parameters are rate i = 0.18 and the number of compounding periods q = 12. Then the annual percentage rate (APR) r is given by
r = (1+[i/q])q-1,
= (1+[0.18/12])12-1,
= (1.015)12-1,
= 0.195618...,
or an APR of 19.5618%.

- anonymous

from http://mathforum.org/dr.math/faq/faq.interest.html

- anonymous

I'm still confused on how I can get the total cost of the purchase.

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- anonymous

I mean, I already know that the APR on the credit card is 27.3% compounded monthly, but how do I get the total cost of the purchase using the APR? Gosh, I'm just confused :/

- phi

one way to do this is figure out the interest on the purchase price $552.86 for one month. then use the payment 195 to pay that interest. use what ever is left over to pay down the purchase price. Now do that for the next month.
I think it only takes a few payments to pay off the whole thing.
Keep track of how much is paid each month to get the total cost

- anonymous

What???? :/

- mathstudent55

She makes the purchase for $552.86.
After one month, she owes $552.86 + the interest of that month.
One month's interest is 27.3%/12 on the balance, so $552.86 * 0.273/12 = $12.58
At the end of the first month, she owes $552.86 + $12.58 = $565.44.
She pays $195. Now she owes $565.44 - $195 = $370.44
After the second month, she owes $370.44 + interst of that month.
One month's interest is 27.3%/12 on the balance, so $370.44 * 0.273/12 = $8.43
At the end of the second month, she owes $370.44 + $8.43 = $378.87
She pays $195. Now she owes $378.87 - $195 = $183.87
After the third month, she owes $183.87 + interest of that month.
One month's interest is 27.3%/12, so $183.87 * 0.273/12 = $4.18
At the end of the third month, she owes $183.87 + $4.18 = $188.05
She pays $188.05 and pays it off.
The total amount she paid was $195 + $195 + $188.05 = $578.05

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