"Your holiday ski vacation was great, but it unfortunately ran a bit over budget. All is not lost. 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 9.4 percent. You plan to make payments of $510 a month on this debt. How many less payments will you have to make to pay off this debt if you transfer the balance to the new card

Explanation:

Let To denote the number of months it would take to reimburse the $10,000

with the old credit card. Then To is such that

5,000 =( 510x(1-(1/(1+.187/12)))To )/.187/12

To=ln (1/(1−(5,000×.187/12)/510))/ln(1 + .187/12)

To =10.72 months

Let Tn denote the number of months it would take to repay the loan with the new credit

card. Assuming that there is no fee on balances transfer, Tn is found by replacing .119

with .094 in the last equation, which gives us

Tn=ln (1/(1−(5,000×.094/12)/510))/ln(1 + .094/12) =10.24months

answer; importance to people; or acceptance;

answernaturalistic observation;