SOLUTION: You can earn 5% per year compounded annually for the next 4 years, followed by 8% per year compounded quarterly for 5 years. What is the average annual compounded rate of return o

Question 883541: You can earn 5% per year compounded annually for the next 4 years, followed by 8% per year compounded quarterly for 5 years. What is the average annual compounded rate of return over the 9 year period? Express your answer with monthly compounding
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
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

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