Question

Helen recently received a credit card with a nominal interest rate of 19 percent. With the card, she purchased some new clothes for $400. The minimum payment on the card is only $20 per month. If Helen makes the minimum monthly payment and makes no other charges, how long will it be before she pays off the card?

Answer 1

Solution:-

PV Ordinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]
C = Cash flow per period
i = interest rate
n = Number of payments
400= 20*((1-(1+ 19/1200)^(-n*12))/(19/1200))
400=20*(1-(1+0.01583)^(-n*12))/0.0153))
400=20*(1-(1.0153)^(-n*12))/0.0153))
400*0.0153=20(1-1.0153)^-n*12
=20(1-(1.0153)^-n*12)/6.12
=3.26(-0.0153)^-n*12))
=3.26-1.64
=1.62
n(in years) = 1.62
months = years*12 = 1.62*12 = 19.44 months