There is a forum with same question but in different perspective.

Question:
if 1000 is invested today and 1000 is invested at the.beginning of each of the next 3 year ar 12% interest(compounded annually), the amount an investor will have at the end of the forth year will be closest to:

It is easy to calculate with calculator in mind like change setting to begin then use N = 4

But if i draw the cash flow
Invest 1000 in beginning of next 3 year. It means that we invest at t=0 t=1 t=2 1000 each ,doesnt it?
and invest today 1000 which mean we invest inaddition 1000 at t=0

My cash flow will be 2000 at t= 0 1000 at t= 1 and 1000 at t=2

If this cashflow is correct, the calculation would be change to begin pmt = 1000 n = 3 cpt PV
Then add addtion 1000
Then use PV find FV (*1.12)^4
Answer is 5806 which is incorrect.

I know that the correct cash flow in answer is 1000 at each t from t= 0 to t= 3.

However, i couldnt figure whats wrong with the mindset behind my cashflow. Can anyone help me plz

Ps. Invest to day t = 0 isnt it?
Ps2. Invest next year but at the beginning of year is equal to invest today isnt it?

Think of it this way: I deposit 1,000 today, which is the beginning of the FIRST whole year. In addition, I deposit 1,000 at the start of the next 3 whole years. (second, third, and fourth). This leads to the deposits happening at exactly times 0, 1, 2, and 3.

On the BAII:

P/Y = C/Y = 1
BGN
4 N 12 I PMT 1000 CPT FV -5,352.8473

Your setup is identical to a 3 year immediate annuity with CFs and times 1, 2, and 3, with an additional 1,000 at time 0. END will give you the future value at time 3, which is 4,779.328; multiplying by 1.12 advances the future value to 5,352.8473.

A lot of extra steps that takes away valuable time from other questions in the exam. Just sayinâ€™â€¦

So first i want thank you for ur help now im understanding more and more but can u plz explain this question too it could be great help for me

If $10,000 is invested today in an account that earns interest at a rate of 9.5%, what is the value of the equal withdrawals that can be taken out of the account at the end of each of the next five years if the investor plans to deplete the account at the end of the time period?
PV = -10,000; I/Y = 9.5; N = 5; FV = 0; CPT â†’ PMT = $2,604.36

So my question is the first question i asked is using today and â€śbeginningâ€ť of next 3 years and for this question the time line is today and the â€śendâ€ť of next 5 years. Although one is invested and one is taken out but the cash flow is seemed to be the same.
With t=0 then t = 1 to 3 in first question
And t=0 then t = 1 to 5 in second question

Isnt beginning of the year and end of the year suppose to have diffirent cash flow? Why when it include timeline of today it has no diffirent result.

Think of it this way: you are sitting at time 0 looking at the future. You still have to go through all of year 1 before you get the first payment. Of course, you still have all of years 2-5 to go through as well.