Determine the cost of credit for a two-year $5000 credit card along with a monthly payment of $257.67, which corresponds to a fixed compounded interest rate of 21.3% compounded monthly round your answer to two decimal places as needed
To determine the cost of credit for a two-year $5000 credit card with a monthly payment of $257.67 and a fixed compounded interest rate of 21.3% compounded monthly, we can use the formula for the future value of an annuity:
PV = PMT * ((1 - (1 + r)^(-n)) / r)
Where:
PV = present value (in this case, the initial credit card balance)
PMT = monthly payment
r = interest rate per period (monthly in this case)
n = total number of periods (in this case, the number of months for two years is 24)
Plugging in the given values:
PV = $5000
PMT = $257.67
r = 21.3% / 100 / 12 = 0.01775 (interest rate per month)
n = 24
PV = $257.67 * ((1 - (1 + 0.01775)^(-24)) / 0.01775)
Evaluating this equation, the present value (initial credit card balance) is approximately $5376.84.
The cost of credit can be calculated as the difference between the total amount paid towards the credit card (the sum of all monthly payments) and the initial credit card balance.
Cost of credit = (Total amount paid) - (Initial credit card balance)
Total amount paid = PMT * n
Total amount paid = $257.67 * 24 = $6184.08
Cost of credit = $6184.08 - $5000 = $1184.08
Therefore, the cost of credit for the two-year $5000 credit card is approximately $1184.08.