I'm having trouble with this question.

A signs a one-year note for $1000 and receives $920 from the bank. At the end of six months, A makes a payment of $288. Assuming simple discount, to what amount does this reduce the face amount of the note?

According to the textbook, the answer is $700, which I got. I first found the simple discount rate from the equation 1000(1-d)=920 and got d=8%. The payment of $288 A made six months into the year would then increase to 288/(1-.08*.5)=$300 at the end of the year. Therefore, A now has to pay only $700 at the end of the year. So I managed to get the right answer, but I don't understand the problem conceptually.

Conceptually, the problem is saying the bank is loaning A a certain amount of money, and for this loan, it is charging a fee (the interest, or discount in this case, I suppose). So A has to pay back the amount he received as well as the discount on top of that at the end of the year. The bank needs to receive $1000 by the end of year. My first instinct was to say since A paid $288, he still needs to pay 1000-288=$712 by the end of the year, and now I'm second-guessing myself because this seems correct. Why would the $288 grow at all (in my solution, I simply applied the discount rate to it, saying it would grow to $300 by the end of the year)? My understanding is that the discount is applied by the bank to the loan it gave A. Why would that same discount rate be applied the other way around, to the money A gives the bank? Like, in my head, only the amount of money A must give to the bank is greater than the amount he borrowed because of the "fee" the bank charges. Why would the money A gives the bank grow? Are we assuming that the bank will take this $288 and immediately reinvest somewhere else at the exact same discount rate (why would it be the same rate?) and then say "Yeah A, the $288 you gave us halfway through the year is the same as giving us $300 at the end of the year, so you only have to give us $700 at the end of the year now"?

Long question, but I hope you get my point. I'm not getting the underlying ideas behind the question.