Why is the annual interest rate more important to a borrower who carries a balance than to a borrower who pays off the
balance monthly?

Step-by-step explanation:

Who is paying is not as important as the interest rate. Either way, a lower rate will benefit the person who has the bill.

Interest to be paid will keep on reducing each month due to reduction of the principal amount.As a result the net interest outgo will be higher for a borrower who carries balance for the whole year compared to one who pays offs monthly.

Step-by-step explanation:

The interest outgo for any balance depends on 3 things:

In case of borrower who carries the balance, the annual interest is:

On the other hand, a borrower who pays the balance monthly,will have a reducing balance on which interest in computed each month. For example,

Month 1 : Interest is computed on entire amount P

Month 2: Interest is computed on

Month 3: Interest is computed on

and so on.

So the interest to be paid will keep on reducing each month due to reduction of the principal amount.

As a result the overall interest outgo at the end of the year will be less compared to the borrower who carries the balance.