Interest Rate Calculations on Credit Card Balance
What is the effective annual interest rate for a credit card with 18% annual interest rate, compounded daily? What is the effective monthly interest rate in the same scenario? How much would the monthly payments be to pay off a $2000 credit card balance in 1 year with equal monthly payments? And how long (in months) will it take to pay off the credit card debt with monthly payments of $125?
The effective annual interest rate for a credit card offering 18% annual interest rate, compounded daily is 18.79%. The effective monthly interest rate is approximately 1.45%. To pay off a $2000 credit card balance in 1 year with equal monthly payments, the monthly payments would be approximately $182.35. If you make monthly payments of $125, it will take you approximately 19 months to pay off the credit card debt.
Calculation Details:
Effective Monthly Interest Rate: To find the effective monthly interest rate, we use the formula: Effective Monthly Rate = (1 + Effective Annual Rate)^(1/12) - 1 The effective monthly rate is approximately 1.45%.
Monthly Payments for $2000 Balance: Using the formula for monthly payment on a loan: Monthly Payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1) The monthly payments to pay off a $2000 balance in 1 year would be approximately $182.35.
Months to Pay off with $125 Monthly Payments: By rearranging the formula to solve for the number of months: n = log(1 - (P * r) / M) / log(1 + r) It will take approximately 19 months to pay off the credit card debt with monthly payments of $125.
These calculations assume a 365-day year and 30-day months, accounting for variations in month lengths.