Question

Your parents have a credit card with a balance of $3,287.90 at an interest rate of 14.5% APR. They pay $1,200.00 each month on the due date until the card is paid off. How many months does it take to pay off the card, and what is the total amount paid including interest? ​

Answer 1

It will take them approximately 3 months to pay off the balance on the credit card

First Month

To solve this problem, we need to find the interest on 3287.90 at 14.5%

for the first month, we would have

$\frac{x}{3287.90}=\frac{14.5}{100} \\x=476.74$

Now we divide this by 12 to give the interest payable on the first month

$\frac{476.75}{12}=39.73$

So we have

$(3287.90+39.73)-1200=2127.63$

Second Month

We would do the same thing for the second month and it will give us

$(\frac{x}{2127.63}=\frac{14.5}{100})/12\\\frac{308.506}{12}=25.71$

For the second month, we have $25.71 as the interest payable

We can calculate how much would be left after the second month.

$(2127.63+25.71)-1200=953.34$

Third Month

In the third month, since the balance remaining is less than the monthly payment schedule, we can assume they'd pay everything off which is 953.34.

From the calculations above, we can see that it'll take them 3 months to pay off the credit card balance.

The balance at the end of each month are;

• $2,127.63
• $953.34
• $0

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