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Line 1: In actuarial mathematics, the '''accumulation function''' ''a''(''t'') is a function of time ''t'' expressing the ratio of the value at time ''t'' ([[future value]]) and the initial investment ([[present value]]).<ref name="Vaaler2009">{{cite book \|last1=Vaaler \|first1=Leslie Jane Federer \|last2=Daniel \|first2=James \|title=Mathematical Interest Theory \|date=19 February 2009 \|publisher=MAA \|isbn=978-0-88385-754-0 \|page=11-61 \|url=https://books.google.com/books?id=1lLsmGVj2HIC~~&pg=PA62~~&dq=%22accumulation+function%22&hlpg=~~en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjW1MvvmZOLAxXYweYEHZVSHMIQ6AF6BAgGEAM#v=onepage&q=%22accumulation%20function%22&f=false~~PA62 \|language=en}}</ref><ref name="Chan2021">{{cite book \|last1=Chan \|first1=Wai-sum \|last2=Tse \|first2=Yiu-kuen \|title=Financial Mathematics For Actuaries ~~(Third Edition)~~ \|date=14 September 2021 \|publisher=World Scientific \|isbn=978-981-12-4329-5 \|page=2 \|edition=Third \|url=https://books.google.com/books?id=VoZGEAAAQBAJ~~&pg=PA2~~&dq=%22accumulation+function%22&hlpg=~~en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjW1MvvmZOLAxXYweYEHZVSHMIQ6AF6BAgMEAM#v=onepage&q=%22accumulation%20function%22&f=false~~PA2 \|language=en}}</ref> It is used in [[interest theory]]. Thus ''a''(0) = 1 and the value at time ''t'' is given by:

Accumulation function: Difference between revisions