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As in this answer, it is written that we have to switch in the BGN mode but in my knowledge if we do in BGN mode then the FV will come out for 11 year and then the next PV should be for 9 years instead of 10. Also in the question it was return that the investment is starting from today so why we are going for the BGN mode instead of END mode…. Please if any one can explain me this that will be great…

At first I thought answer should be option B, but the solution provided is absolutely right.
The question says that annual payment of 1000 starts today and there will be 10 equal payments which means annuity starts at 0 and continues to 9 (i.e. 10 payments),
thus beginning anuity is appropriate and the FV of this will come on 10 (not on 11).
End mode use nahi karenge bz annuity payment is starting today. This question is a tricky one.
Nothing tricky, but it require you to think about when the cashflow is taking place, where the FV will come.
BGN mode me t+1 pe FV ayega, BGN me krne se 10 PMT ka FV value at t=11 kpe aya means 10th year k end me aya means begining of 11. ab 11 k starting se 20 k end tk 10 years hai to fir se N=10 hoga.
but this time END mode and BGN mode same ayega. Because BGN ka 10 complete hoga 20 k begining me and value aya 20 k end me ie, t+1
and END mode se to FV comes at t=T ie, at the end of 20.
Ans ka strokes dene ka koi matlab nhi answer me diya hai already, bss concept thora explain kiye, samjh me aya ki nhi batana !!
mera answer correct aaya tha, but your explanation made it revise all. Thank you.