document.write( "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 \n" ); document.write( "
Algebra.Com's Answer #533597 by LinnW(1048)\"\" \"About 
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Assume we start with $100
\n" ); document.write( "Value after 4 year = 100*(1.05)^4
\n" ); document.write( "(100*(1.05)^4)*(1.08)^5 = 178.5977
\n" ); document.write( "Let x = the average return
\n" ); document.write( "(100)*(1+x)^9 = 178.5977
\n" ); document.write( "divide each side by 100
\n" ); document.write( "(1+x)^9 = 1.7805977
\n" ); document.write( "Take the 9th root of each side
\n" ); document.write( " 1+x = 1.7805977^(1/9)
\n" ); document.write( "add -1 to each side
\n" ); document.write( " x = -1 + 1.7805977^(1/9)
\n" ); document.write( " x = 0.06620489
\n" ); document.write( "Let's check
\n" ); document.write( "(100)*(1.06620489)^9 = 178.05986
\n" ); document.write( "so we are pretty close
\n" ); document.write( "Let's bump up our rate to 0.0665
\n" ); document.write( "(100)*(1.0665)^9 = 178.5039
\n" ); document.write( "It appears that the average rate is close to 6.65 %
\n" ); document.write( "Some of the differences in calculation are probably rounding error.
\n" ); document.write( "www.wolframalpha.com was used for calculation
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