document.write( "Question 613671: How long does it take a $2800 investment to double if it's invested at 8% compounded quarterly? \n" ); document.write( "
Algebra.Com's Answer #386141 by Theo(13342)\"\" \"About 
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f = p*(1+(i/c))^y*c
\n" ); document.write( "f = future value
\n" ); document.write( "p = present value = 2800
\n" ); document.write( "i = 8% per year.
\n" ); document.write( "c = 4
\n" ); document.write( "y = number of years
\n" ); document.write( "i/c = 2% per quarter = .02
\n" ); document.write( "1 + i/c = 1.02
\n" ); document.write( "n = y*c = number of years * compounding periods per year.
\n" ); document.write( "your formula becomes:
\n" ); document.write( "f = 2800 * (1.02)^n
\n" ); document.write( "since you want the future value of your principal to double, then:
\n" ); document.write( "f = 2*2800 = 5600
\n" ); document.write( "your formula becomes:
\n" ); document.write( "5600 = 2800 * (1.02)^n
\n" ); document.write( "divide both sides of this equation by 2800 to get:
\n" ); document.write( "2 = (1.02)^n
\n" ); document.write( "take the log of both sides of this equation to get:
\n" ); document.write( "log(2) = log(1.02^n)
\n" ); document.write( "this becomes:
\n" ); document.write( "log(2) = n*log(1.02) based on properties of logarithms.
\n" ); document.write( "divide both sides of this equation by log(1.02) to get:
\n" ); document.write( "log(2) / log(1.02) = n
\n" ); document.write( "solve for n using the LOG function of your calculator to get:
\n" ); document.write( "n = 35.00278878
\n" ); document.write( "it take 35.00278878 quarters for your money to double.
\n" ); document.write( "this equates to 35.00278878/4 = 8.750697195 years.\r
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