Damian has a balance of $10,200 on his credit card. He threw the card away so he can never use it again. He has 3.5 years to pay off the balance. The interest rate on his card is 21%.
Part A) At the end of the 3.5 years, how much interest has he paid?
Part B) When Damian pays off his credit card, how much he will have paid in all?
Part A) To calculate the total interest paid, we first need to calculate the monthly interest rate.
Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 21% / 12 = 1.75%
Next, we need to calculate the total interest paid over 3.5 years (42 months). We will use the formula for calculating compound interest:
Interest = Principal x ((1 + r)^n - 1)
where:
- Principal = $10,200
- r = monthly interest rate (1.75% or 0.0175)
- n = number of periods (42 months)
Interest = $10,200 x ((1 + 0.0175)^42 - 1)
Interest = $10,200 x (1.0175^42 - 1)
Interest = $10,200 x (1.864755 - 1)
Interest = $10,200 x 0.864755
Interest = $8,830.83
Damian will have paid $8,830.83 in interest at the end of 3.5 years.
Part B) To calculate the total amount paid, we add the initial balance and the total interest paid:
Total amount paid = Initial balance + Total interest paid
Total amount paid = $10,200 + $8,830.83
Total amount paid = $19,030.83
Damian will have paid a total of $19,030.83 when he pays off his credit card.