I am really confused about this question of when to use BGN mode and when to use END mode and what should we take the value of N while calculating PV of annuity i.e. N=26 or 25.

please help me with this question if anyone can give brief answer it would be helpful for me

Sure, I can help you with an annuity question related to Time Value of Money (TVM). Annuities involve a series of equal payments made or received at regular intervals over time. What specific annuity question do you have? Please provide more details so I can assist you effectively.

Regarding the question I have posted (image attached in the question) over there I am confused about what to take N while calculating the PV of annuity 210000 should we take N as 25 or 26? As the annuity payment will start 15 years from now at the beginning of each year till the person dies i.e. 40 years from now. So what should we take N as

you should take N = 25 , because its an annuity due ,so first annuity is at t=15 (beginning of year 16)

and last annuity is at t=39 (beginning of year 40) . take fv = 18,00,000 / pmt = 2,10,000 / i/y = 8 and pv will be = 26,83,871.46 .

Now in End mode (ordinary annuity) calculate the annuity amount by taking .

fv = 26,83,871.46 / n = 15 / i/y = 10 / pmt will be = 84,471.56 .

the trick to find N in annuity sum is to look for the no. of payments to be made . in this sum the payments is second annuity is 25 ( from t = 15 to t = 39 ) if you count from 15 to 39 you will get 25 N ….if you do subtraction like (39 -15) then add 1 to the answer so 24+1 = 25 . bcz when we subtract we do not count the another value .

If i made any mistakes while explaining please feel free to correct me .

if u draw the timeline, he needs $210,000 at t=15 until t=40 for 25 years, here we use BGN mode as he needs the annuity at start, therefore we calculate PV of annuity which is $2,421,071. we do clear tvm as we also need to bring to t=15, the present value of $1.8m after he passes away at t=40, which when discounted by 8% comes to 262,832 (this should be done in END mode).

the sum of the two cashflows shall be the FV of annuity beginning from end of year 1.

we set to END mode and set FV to ($2,421,071+$262,832 = $2,683,903), N=15, I/Y = 10 and we compute PMT which works out to be Option A