Question 883541
Assume we start with $100
Value after 4 year = 100*(1.05)^4
(100*(1.05)^4)*(1.08)^5 = 178.5977
Let x = the average return
(100)*(1+x)^9 = 178.5977
divide each side by 100
(1+x)^9 = 1.7805977
Take the 9th root of each side
 1+x = 1.7805977^(1/9)
add -1 to each side
  x = -1 + 1.7805977^(1/9)
  x = 0.06620489
Let's check
(100)*(1.06620489)^9 = 178.05986
so we are pretty close
Let's bump up our rate to 0.0665
(100)*(1.0665)^9 = 178.5039
It appears that the average rate is close to 6.65 %
Some of the differences in calculation are probably rounding error.
www.wolframalpha.com was used for calculation