Question

Suppose your credit card balance is $15,500. The minimum payment is $322, and the annual percentage rate is 19.1%. a. If you make a constant monthly payment of $322, how long will it take you to pay off the credit card balance? b. How much interest will you pay if you elect to make the minimum payment? a. If you make a constant monthly payment of $322, how long will it take you to pay off the credit card balance? months (Round to four decimal places)

Answer 1

(a) Loan Amount = P = $15500

Interest Rate = 19.1% or 0.191/12 monthly

Number of payment periods = n months

Monthly payments made be X = $322

Hence, the sum of present value of monthly payments must be equal to the value of the loan amount

=> X/(1+r) + X/(1+r)² +....+ X/(1+r)^N = P

=> X[1- (1+r)^-N]/r = P

=> [1- (1+r)^-N] = Pr/X

=> (1+r)^-N = 1 - Pr/X

=> N = - ln (1 - Pr/X) / ln (1+r) = - ln (1 - 15500*(0.191/12)/322) / ln (1 + 0.191/12) = 92.0241 months

(b) Interest Paid = Number of months * Monthly Installments - Loan Amount

= 92.0241*322 - 15500

= $14131.7602