How does an extra investment $X into the economy in 2005 effect the GDP in 2009.?

Question

assuming investment $X is spent on infrastructure that takes effect immediately. GDP deflator for 2005 and 2009 are given to be 100 and 115 respectively and multiplier is 5.

Answer 1

I think that would depend on a lot of factors.  For instance, age and education of your workforce, etc.  

Answer 2

Depends on model you will use, for simple Keynesian cross increase in real GDP will be: ΔY=ΔI * 5 = +5 * $X.

So if initial RGDP(2005) was $Y then RGDP(2009)= $Y + 5* $X.

(under "ceteris paribus" conditions).

And Nominal GDP NGDP(2009)=($Y + 5*$X)*1.15

Actually don't forget that RGDP(2006!)=($Y + 5* $X)=RGDP(2007!)=RGDP(2008!)=RGDP(2009!) because it is set by initial task by words "that takes effect immediately" and there is no additional information about growth rates and other factors.