Question

You just received an offer in the mail to transfer your $5,000 balance from your current credit card, which charges an annual rate of 18.7 percent, to a new credit card charging a rate of 7.9 percent. You plan to make payments of $250 a month on this debt. How many fewer payments will you have to make to pay off this debt if you transfer the balance to the new card?

A 2.48

B 2.63

C 3.10

D 2.79

E 2.86

Answer 1

Monthly Payment = rP(1+r)^N/[(1+r)^N-1]

where, r is the monthly interest rate

N is the number of periods

P is the borrowed amount

Monthly Payment in both cases is $250

When r = 18.7% or 0.187,

250 = (0.187/12)*5000*(1+0.187/12)^N1/((1+0.187/12)^N1-1)

=> ((1+0.187/12)^N1-1) = 0.3117*(1+0.187/12)^N1

N1 = 24.15 months

when, r = 7.9%

250 = (0.079/12)*5000*(1+0.079/12)^N2/((1+0.079/12)^N2-1)

=> N2 = 21.52

N1- N2 = 24.15 - 21.52 = 2.63 months

Hence, correct option is (b) 2.63