document.write( "Question 1188726: How long will it take Php 2000 to earn Php 500 if the interest is 12% compound monthly \n" ); document.write( "
Algebra.Com's Answer #819877 by Theo(13342)\"\" \"About 
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the interest is 12% compounded monthly.
\n" ); document.write( "diviee that by 12 to get an interest of 1% per month.
\n" ); document.write( "divide that by 100 and add 1 to it to get a growth rate of 1.01 per month.
\n" ); document.write( "to earn an interest of 500, the 2000 must grow to 2500.
\n" ); document.write( "your equation is 2500 = 2000 * 1.01 ^ n
\n" ); document.write( "n is the number of months.
\n" ); document.write( "divide both sides of that equation by 2000 to get:
\n" ); document.write( "2500 / 2000 = 1.01 ^ n
\n" ); document.write( "simplify to get:
\n" ); document.write( "5/4 = 1.01 ^ n
\n" ); document.write( "take the log of both sides of the equation to get:
\n" ); document.write( "log(5/4) = log(1.01 ^ n) which becomes:
\n" ); document.write( "log(5/4) = n * log(1.01)
\n" ); document.write( "divide both sides of that equation by log(1.01) to get:
\n" ); document.write( "log(5/4) / log(1.01) = n
\n" ); document.write( "solve for n to get:
\n" ); document.write( "n = 22.42574188\r
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\n" ); document.write( "\n" ); document.write( "it will take 22.42574188 months to earn 500 interest on the account.
\n" ); document.write( "2000 * 1.01 ^ 22.42574188 = 2500
\n" ); document.write( "2500 - 2000 = 500 interest.\r
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