can someone please help me to understand the timeline? Sometimes I get it right and others, I can’t figure out if I have to use annuity due! Like in the below question, does the 5th year include in 7 years? Or 7 years starts from 6th year?
An investor will receive an annuity of $5,000 a year for seven years. The first payment is to be received 5 years from today. If the annual interest rate is 11.5%, what is the present value of the annuity?
answer: $15,000
Similarly, another question, how would you know if you have to use annuity due in this one:
How much should an investor have in a retirement account on his 65th birthday if he wishes to withdraw $40,000 on that birthday and each of the following 14 birthdays, assuming his retirement account is expected to earn 14.5%?
answer: $274,422
thanks so much for your help!
For the first problem, you could treat it like an annuity due at time 5 or an immediate annuity at time 4. Better way is to use the C.F. worksheet: saves you a lot of key strokes!!! 
For the 2nd problem, it screams annuity due!!!
Hi,
Thanks very much. For the first problem, I used C.F worksheet F01=5, it didn’t give me a correct answer but when I used F01=4, it did. So, in conclusion, CF0=0 is considered one year and on top 4 more years.
For question 2, could you please elaborate more how it is annuity due? Is it because the question says, on his 65th birthday and each of the following birthdays?
Have a great day!
Good morning!!!
Treat C0 in the CF worksheet as being time 0, i.e. now. The next entries would be time 1, 2, 3, etc. If F01=4, then C02 would happen at time 5. 
For an annuity due, the focal date of the equation happens to be the date of the first payment; for an immediate annuity, the focal date is one period BEFORE the first payment. Since we need to know the PV right at age 65 when the first payment occurs, therefore we use the annuity due formula.
Thanks million for the explanation.
Enjoy rest of your day!