First, we need to calculate the monthly interest rate by dividing the APR by 12:
11.99% / 12 = 0.9992%
Next, we can use the formula for monthly interest on credit cards, which is:
(balance x monthly interest rate) + (payment - (balance x monthly interest rate)) = new balance
We can solve for the new balance each month, and then use the new balance to calculate the interest for the following month. Here's how it works:
Month 1:
(balance x 0.9992%) + ($350 - (balance x 0.9992%)) = $7,219.17 (new balance)
Month 2:
($7,219.17 x 0.9992%) + ($350 - ($7,219.17 x 0.9992%)) = $6,870.19 (new balance)
Month 3:
($6,870.19 x 0.9992%) + ($350 - ($6,870.19 x 0.9992%)) = $6,516.76 (new balance)
Month 4:
($6,516.76 x 0.9992%) + ($350 - ($6,516.76 x 0.9992%)) = $6,158.68 (new balance)
Month 5:
($6,158.68 x 0.9992%) + ($350 - ($6,158.68 x 0.9992%)) = $5,795.73 (new balance)
Month 6:
($5,795.73 x 0.9992%) + ($350 - ($5,795.73 x 0.9992%)) = $5,427.67 (new balance)
Month 7:
($5,427.67 x 0.9992%) + ($350 - ($5,427.67 x 0.9992%)) = $5,054.24 (new balance)
Month 8:
($5,054.24 x 0.9992%) + ($350 - ($5,054.24 x 0.9992%)) = $4,675.18 (new balance)
Month 9:
($4,675.18 x 0.9992%) + ($350 - ($4,675.18 x 0.9992%)) = $4,290.23 (new balance)
Month 10:
($4,290.23 x 0.9992%) + ($350 - ($4,290.23 x 0.9992%)) = $3,899.12 (new balance)
Month 11:
($3,899.12 x 0.9992%) + ($350 - ($3,899.12 x 0.9992%)) = $3,501.61 (new balance)
At the end of the 11th month, the balance is paid down to $3,501.61, and then at the end of the 12th month, it is paid off completely.
To calculate the total interest paid, we can add up the interest for each month:
$7,568.19 - $7,219.17 = $349.02
$7,219.17 - $6,870.19 = $348.98
$6,870.19 - $6,516.76 = $353.43
$6,516.76 - $6,158.68 = $358.08
$6,158.68 - $5,795.73 = $362.95
$5,795.73 - $5,427.67 = $368
I explained step by step.