Dear Kathleen,
I am writing to tell you my news. My school has chosen me to spend six weeks at a school in the USA. I'm very happy about it!
At the moment, I am packing things for my trip, because I am leaving next week. My mother has booked the ticket.
I have been waiting for this opportunity for ages, so I'm very excited. I have finished reading two books about the USA, and I have borrowed another one from the school library. I am becoming more and more nervous every day.
Well, I must go now. I've got a lot of things to do. I'll write to you from the USA.
Love,
Tracy
Here's the expanded explanation for each verb form used in the letter:
"I am writing" - Present Continuous tense is used here because the action of writing is happening at the moment of speaking.
"has chosen" - Present Perfect tense is used to indicate that this event happened at an unspecified time in the past, but it has a relevance to the present moment.
"am packing" - Present Continuous tense indicates that the action of packing is currently in progress.
"am leaving" - Present Continuous tense is used for a planned future event. Here, it means that the decision and plan to leave are already set.
"has booked" - Present Perfect tense is used to show that the action of booking happened at some unspecified time before now and is relevant to the current situation.
"have been waiting" - Present Perfect Continuous tense is used to emphasize the duration of the action that started in the past and continues up to now, reflecting Tracy's anticipation.
"have finished" - Present Perfect tense again, indicating the completion of reading two books at some unspecified time before now.
"have borrowed" - Present Perfect tense used to show the action's relevance to the present moment, indicating that Tracy currently has the book from the library.
"am becoming" - Present Continuous tense is used to describe a gradual change or development in Tracy's emotional state.
This complete answer provides context to the grammatical choices made in the sentences and explains the usage of different tenses in detail.