document.write( "Question 1090057: You have two investments. One you put $5,000 into that returns 10% compounded quarterly. The other investment you $10,000 into that returns 5% compounded quarterly. Will these two investments ever be worth the same amount? If so, in what month? \n" ); document.write( "

Algebra.Com's Answer #704484 by Boreal(15235) $\"\"$ $\"About$

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one is 5000(1+.025)^4n
\n" ); document.write( "other is 10000(1+.0125)^4n
\n" ); document.write( "this is equivalent to (1.025)^n and 2(1.0125)^n
\n" ); document.write( "The first should catch the second at some point.
\n" ); document.write( "set them equal.\r
\n" ); document.write( "\n" ); document.write( "10000(1.0125)^n=5000(1.025)^n
\n" ); document.write( "2(1.0125)^n=1.025^n
\n" ); document.write( "2=(1.025/1.0125)^n
\n" ); document.write( "ln both sides
\n" ); document.write( "ln2= n ln (1.025/1.0125)=n*0.012227
\n" ); document.write( "0.693=0.012227 n
\n" ); document.write( "n=56.49 quarterly compoundings or just over 14 years or 168 months
\n" ); document.write( " $\"graph%28300%2C300%2C50%2C60%2C-10%2C10%2C1.025%5Ex%2C2%2A%281.0125%29%5Ex%29\"$
\n" ); document.write( " $\"graph%28300%2C300%2C-10%2C70%2C-10%2C10%2C1.025%5Ex%2C2%2A%281.0125%29%5Ex%29\"$ \n" ); document.write( "

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