Rainbow Annuities (Society of Actuaries Exam FM - Financial Mathematics - Module 2, Section 7)

[@johnnaivest1284]

Wow. Thank you Prof. Paris. Actually, i was struggling with the long formula. it was indeed wasting my limited time.

[@racool911]

Do you know where I can find a derivation of this?

[@ciroweinstein8627]

Thankyou!!

[@analystprep]

You're welcome!

[@natjimoEU]

Why would u not derive it?

[@Chichi0104]

Hie Prof,could you please help me understand why we used v^n in 2.08'

[@MrSherman51]

The Ds is valued at that time. You need to bring it back to the PV time in the beginning.

[@yaweli2968]

Someone answered your question. If you look at the first n payments as increasing annuity, there will be n-1 payments left as decreasing annuity due. But you can only add two amounts up in the same time value,so you need to discount the n-1 decreasing sum back to the valuation date of the annuity due, which is n periods back, so you multiply by v^n.