Like many college students, Dana applied for and got a credit card that has an a

Question

Like many college students, Dana applied for and got a credit card that has an annual percentage rate (APR) of 15% The first thing she did was buy a new HD Television for $250. At the end of the month, her credit card statement said she only needed to make a minimum monthly payment of $15. Assume Dana makes her payment when she sees her statement at the end of each month. If Dana doesn't charge anything else and only makes the minimum monthly payments, approximately how many months would it take her to completely pay off the HD Television? Assume that the credit card company compounds interest at the end of each month O 46.3 months O 18.8 months 32.6 months 37.8 months O 19.3 months Dana now realizes she needs to pay more than just the minimum payment (unless she wants to be paying for this HD Television until she graduates). She decides to pay twice the minimum monthly payment ($30 per month), instead How much quicker will she pay off the HD Television? O 19.5 months O 26.4 months O 10.3 months O 9.9 months O 16.8 months If, instead, Dana wants to have the HD Television paid for by the end of the year, what minimum monthly payment must she make? O $31.59 O $32.09 O $22.56 O $36.10 O $23.92

Explanation / Answer

Answer 1 Using present value of annuity formula we can find out the no.of months it will take to pay off the HD television Present value of annuity = P x [1 - (1+r)^-n]/r] Present value of annuity = $250 P = Monthly payment = $15 r = month per APR = 15%/12 = 0.0125 n = no.of months = ? 250 = 15 x [1 - (1+0.0125)^-n]/0.0125] 16.66 = [1 - (1+0.0125)^-n]/0.0125] n = 18.8 It will take 18.8 months to pay off the HD Television. Answer 2 Present value of annuity = P x [1 - (1+r)^-n]/r] Present value of annuity = $250 P = Monthly payment = $30 r = month per APR = 15%/12 = 0.0125 n = no.of months = ? 250 = 30 x [1 - (1+0.0125)^-n]/0.0125] 16.66 = [1 - (1+0.0125)^-n]/0.0125] n = 8.9 It will take 8.9 months to pay off the HD Television if she pays the twice the minimum monthly payment. She will pay off the loan 9.9 months earliers [18.8 months - 8.9 months] The answer is 9.9 months. Answer 3 Present value of annuity = P x [1 - (1+r)^-n]/r] Present value of annuity = $250 P = Monthly payment = ? r = month per APR = 15%/12 = 0.0125 n = no.of months = 12 250 = P x [1 - (1+0.0125)^-12]/0.0125] 250 = P x 11.07931 P = 22.56 She must make minimum monthly payment of $22.56 to have the HD Television paid for by the end of the year. The answer is $22.56

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