#acl All:read

Link to > CongregationData

== Calculation of probable income loss by deaths ==

The standard life tables come in the form of "the number of persons surviving to exact age x out of 100,000 births".  This is the second column in the table below, the first column being age.

The third column is the probability of surviving 5 years, computed as the number of survivors at Age+5 / survivors at Age.  For example at age 80 the probability of surviving 5 years is Survivors(85)/Survivors(80)=56373/72308=0.779623.

The estimated income in five years as a % of current is then the sum of (%income in each age band) multiplied by the probability of surviving five years in the middle of that age band.  Givers without ages are omitted, assuming that they are similarly distributed.

||Age band||% income||% 5 year survival||Product (% income)||
||<50||10%||99.99%||10%||
||51-60||16%||98%||16%||
||61-70||23%||96%||22%||
||71-80||30%||88%||26%||
||>80||21%||61%||13%||
||Total||99%|| ||87%||

So for example the 30% of current income coming from those in their 70s can be expected to decrease to 26% of current income.

The estimated income in 5 years is then 87% out of the 99% from givers for whom we have ages or estimated ages, or 85% of current income from those givers.  Assuming that those without ages given are similarly distributed, we should expect a 15% reduction in 5 years from deaths.

||<tablewidth="100%" style="border:none;text-align:left;"> This is the giving profile. The blue curve is the distribution of planned givers, the red curve is the distribution of income, and the green curve is the most likely distribution of income in five years time.  ||<style="border:none;text-align:left;">{{attachment:WithFiveYearCurve.jpg}}||

||<tablewidth="100%" style="border:none;text-align:left;"> Repeating the procedure described above year by year for 20 years gives this curve  ||<style="border:none;text-align:left;">{{attachment:ProgressiveGiving.jpg}}||

The data used follows:

||Age||Survivors 1 year||Survival probability 5 years||
||0||100000||0.99482||
||1||99560||0.999106||
||2||99528||0.999327||
||3||99509||0.999437||
||4||99494||0.999508||
||5||99482||0.999558||
||6||99471||0.999598||
||7||99461||0.999628||
||8||99453||0.999628||
||9||99445||0.999608||
||10||99438||0.999547||
||11||99431||0.999437||
||12||99424||0.999286||
||13||99416||0.999105||
||14||99406||0.998924||
||15||99393||0.998783||
||16||99375||0.998682||
||17||99353||0.998621||
||18||99327||0.998601||
||19||99299||0.9986||
||20||99272||0.99857||
||21||99244||0.998549||
||22||99216||0.998508||
||23||99188||0.998468||
||24||99160||0.998397||
||25||99130||0.998336||
||26||99100||0.998264||
||27||99068||0.998173||
||28||99036||0.998071||
||29||99001||0.99796||
||30||98965||0.997838||
||31||98928||0.997675||
||32||98887||0.997522||
||33||98845||0.997329||
||34||98799||0.997125||
||35||98751||0.996881||
||36||98698||0.996616||
||37||98642||0.99632||
||38||98581||0.995983||
||39||98515||0.995615||
||40||98443||0.995205||
||41||98364||0.994775||
||42||98279||0.994292||
||43||98185||0.993777||
||44||98083||0.99323||
||45||97971||0.992651||
||46||97850||0.992018||
||47||97718||0.991353||
||48||97574||0.990643||
||49||97419||0.989889||
||50||97251||0.9891||
||51||97069||0.988266||
||52||96873||0.987334||
||53||96661||0.986282||
||54||96434||0.985057||
||55||96191||0.983647||
||56||95930||0.982029||
||57||95646||0.980219||
||58||95335||0.978266||
||59||94993||0.976177||
||60||94618||0.973937||
||61||94206||0.971552||
||62||93754||0.968983||
||63||93263||0.966128||
||64||92730||0.962914||
||65||92152||0.959263||
||66||91526||0.955051||
||67||90846||0.950212||
||68||90104||0.944653||
||69||89291||0.938303||
||70||88398||0.931073||
||71||87412||0.922917||
||72||86323||0.913731||
||73||85117||0.903415||
||74||83782||0.891767||
||75||82305||0.878537||
||76||80674||0.863488||
||77||78876||0.846303||
||78||76896||0.826714||
||79||74714||0.804521||
||80||72308||0.779623||
||81||69661||0.751884||
||82||66753||0.721361||
||83||63571||0.688128||
||84||60109||0.652382||
||85||56373||0.61439||
||86||52377||0.57468||
||87||48153||0.533923||
||88||43745||0.492925||
||89||39214||0.452491||
||90||34635||0.413426||
||91||30100||0.376312||
||92||25710||0.341579||
||93||21563||0.309512||
||94||17744||0.280207||
||95||14319||0.253789||
||96||11327||0.23007||
||97||8782||0.209064||
||98||6674||0.19059||
||99||4972||0.174377||
||100||3634||0.160429||
||101||2606||0.14812||
||102||1836||0.1378||
||103||1272||0.128931||
||104||867||0.121107||

From Australian Life tables 2005-2007
© Commonwealth of Australia 2009
ISBN 978-0-642-74561-3

DavidMorgan  Dec 2013