Question

Marilyn uses a credit card with a 19.9% APR compounded monthly to pay for car repairs totaling $991.38. She can pay $410 per month on the card. What will the total cost of this purchase be?
a) $1,021.01

b) $1,188.66

c) $991.38

d) $1,192.39

Answer 1

It didn't really say anything about how to do this kind of problem, though =/ thank you, nontheless

Answer 2

$991.38 is charged to her card on day 1

After 1 month, she owes $991.50 + one month's interest on $991.50
One month's interest is: 19.9/100/12 x $991.5 = $16.44
So after the first month she owes $991.50 + $16.44 = $1007.94
She pays $410, so her balance now is $1007.94 - $410 = $597.94

After one more month, her new balance is $597.94 + one month's interest on $597.94
One month's interest is: 19.9/100/12 x $597.94 = $9.92
So after the 2nd month she owes $597.44 + $9.92 = $607.86
She pays $410, so her balance now is $607.86 - $410 = $197.86

After one more month, her new balance is $197.86 + one month's interest on $197.86
One month's interest is: 19.9/100/12 x $197.86 = $3.28
So after the 2nd month she owes $197.86 + $3.28 = $201.14
She pays $201.14, and pays it off.

The total she paid was $410 + $410 + $201.14 = 1021.14

Answer 3

thanks a bunch!

Answer 4

Month 1:

991.38*(1 + 0.199/12) = 1007.82
Make payment: 1007.82 - 410 = 597.82


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Month 2:

597.82*(1 + 0.199/12) = 607.73
Make payment: 607.73 - 410 = 197.73


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Month 3:

197.73*(1 + 0.199/12) = 201.01
Make payment: 201.01


Notice how the balance is less than the monthly payment. So this is when the card will be fully paid off.

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Payments made: 410, 410, 201.01


Add up the payments to get 410+410+201.01 = 1,021.01

Answer 5

So the total cost is $1,021.01

Answer 6

thank you--much appreciated!

Answer 7

yw

Answer 8

I just noticed that I used $991.50 in my fisrt calculation even though I had written $991.38 originally. I just redid it with the correct $991.38.

$991.38 is charged to her card on day 1

After 1 month, she owes $991.38 + one month's interest on $991.38
One month's interest is: 19.9/100/12 x $991.38 = $16.44
So after the first month she owes $991.38 + $16.44 = $1007.82
She pays $410, so her balance now is $1007.82 - $410 = $597.82

After one more month, her new balance is $597.82 + one month's interest on $597.82
One month's interest is: 19.9/100/12 x $597.82 = $9.91
So after the 2nd month she owes $597.82 + $9.91 = $607.73
She pays $410, so her balance now is $607.73 - $410 = $197.73

After one more month, her new balance is $197.73 + one month's interest on $197.73
One month's interest is: 19.9/100/12 x $197.73 = $3.28
So after the 2nd month she owes $197.73 + $3.28 = $201.01
She pays $201.01, and pays it off.

The total she paid was $410 + $410 + $201.01 = 1021.01