Final answer:
To pay off a $2,000 credit card debt at a 17% interest rate in 3 years, the monthly payment would be $71.54. This calculation uses the amortization formula and includes the principal, monthly interest rate, and number of payments.
Step-by-step explanation:
Calculating Monthly Credit Card Payments
To calculate the monthly payment required to pay off a $2,000 credit card debt at a 17% interest rate over 3 years, we'll use the formula for an amortizing loan which factors in the principal, the interest rate, and the number of payment periods. The formula for the monthly payment of an amortizing loan is:
P = [r*PV] / [1 - (1 + r)^-n]
Where:
- P = Monthly payment
- PV = Present value, or principal amount (in this case, $2,000)
- r = Monthly interest rate (annual rate/12; in this case, 17%/12)
- n = Total number of payments (in this case, 3 years * 12 months/year = 36 months)
Applying these values to the formula gives us:
P = [0.17/12 * 2000] / [1 - (1 + 0.17/12)^-36] = $71.54
Thus, you will need to pay $71.54 each month to pay off the $2,000 debt over 3 years, without adding any new charges to the card.