annuities

I do not know what you mean about not having tables - there are tables in the free Course Notes (and you should not be watching the lectures without the course notes in front of you) and you get given tables in the exam. No - you cannot take the discount factor for 1 to 12 instead. That only works if the flow starts in 1 years time. If the flow starts in 3 years time then it will give you a value in 2 years time and you then need to discount for 2 years.

Sir I think I'm missing something very important and my questiom may sound stupid as well but i really dont understand about this and I don't know where am i confused. If our annuity is for 10years so each year we get amount including interest, if we remove the interest from the amounts we get each year and add them up so their sum will be equal to the amout we have deposited right? So given the discout factor of 14 years in the table and we subtract 3years discount factor as it started in the forth year, so using the AFTER substracted discount factor, will it give us the same amount we deposited? Maybe I'm in the complete misconcept or i don't understand this annuity procedure.

I do not understand what you mean - in your first question you were asking about annuity starting in 3 years and finishing in 14 years. Now you are taking about 14 years less 3 years. Have you watched the free lecture on this??