Katherine uses her credit card to purchase a new television for $709.15. She can pay off up to $350 per month. The card has an annual rate of 25.7% compounded monthly.
How much will she pay in interest?
not sure what the exact answer is here you should have stated the answer clearly
interest for 1st month = 709.15(.257)/12 = 15.19
balance at end of 1st month = 709.15 + 15.19 - 350
= 374.34
interest for 2nd month = 374.34(.257)/12 = 8.02
balance at end of 2nd month = 374.34 + 8.02 - 350
= 32.35
interest for 3rd month = 32.35(.257)/12 = .69
amount due = 32.35 + .69
= 33.04
** So the total she paid for her $709.15 TV was
350+350+3304 = $733.04
her interest paid = 733.04 - 709.15 = $23.89
the calculation shown as ** is actually not valid even though it is done all the time. We cannot add up amounts of money that are not at the same "time spot".
e.g. If I deposit $500 now and another $500 two years from now , I will not have $1000 two years from now, unless I totally disregard any interest rate.
Thank you so much for the explanation.
To calculate the total amount of interest Katherine will pay on her credit card, we need to consider the monthly payments she makes and the interest rate charged on the outstanding balance.
First, let's determine how long it will take for Katherine to pay off her credit card debt. She can pay up to $350 per month, and the television costs $709.15. We can divide the total cost of the TV by the monthly payment to find out how many months it will take:
$709.15 / $350 = 2.03 months
Since you cannot have partial months, it will take Katherine 3 months to pay off the TV.
Next, let's calculate the interest charged on the outstanding balance each month. The annual interest rate on the card is 25.7% compounded monthly. To find the monthly interest rate, we divide the annual rate by 12:
25.7% / 12 = 2.14% = 0.0214
Now, we can calculate the interest for each month. To do this, we multiply the outstanding balance at the beginning of each month by the monthly interest rate:
Month 1 interest: $709.15 x 0.0214 = $15.16
Month 2 interest: ($709.15 - $350) x 0.0214 = $7.63
Month 3 interest: $0 (since the balance will be fully paid off)
Finally, we add up the interest charged each month to find the total interest paid:
$15.16 + $7.63 + $0 = $22.79
Therefore, Katherine will pay $22.79 in interest over the 3-month period.