document.write( "Question 218358: $40 at 4% (compounded daily) how long will it take for me to have $50? \n" ); document.write( "
Algebra.Com's Answer #164468 by jim_thompson5910(35256)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "\"A=P%281%2Br%2Fn%29%5E%28nt%29\" Start with the compounding interest formula.\r
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\n" ); document.write( "\n" ); document.write( "\"50=40%281%2B0.04%2F365%29%5E%28365%2At%29\" Plug in \"A=50\", \"P=40\", \"r=0.04\" (note: 0.04 is the decimal equivalent of 4%) and \"n=365\"\r
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\n" ); document.write( "\n" ); document.write( "\"50=40%281%2B0.0001096%29%5E%28365%2At%29\" Divide \"0.04%2F365\" to get \"0.0001096\".\r
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\n" ); document.write( "\n" ); document.write( "\"50=40%281.0001096%29%5E%28365%2At%29\" Add.\r
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\n" ); document.write( "\n" ); document.write( "\"%2850%29%2F%2840%29=%281.0001096%29%5E%28365%2At%29\" Divide both sides by \"40\".\r
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\n" ); document.write( "\n" ); document.write( "\"1.25=%281.0001096%29%5E%28365%2At%29\" Divide \"50%2F40\" to get \"1.25\".\r
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\n" ); document.write( "\n" ); document.write( "\"log%2810%2C%281.25%29%29=log%2810%2C%28%281.0001096%29%5E%28365%2At%29%29%29\" Divide \"50%2F40\" to get \"1.25\".\r
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\n" ); document.write( "\n" ); document.write( "\"log%2810%2C%281.25%29%29=365%2At%2Alog%2810%2C%281.0001096%29%29\" Pull down the exponent.\r
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\n" ); document.write( "\n" ); document.write( "\"log%2810%2C%281.25%29%29%2Flog%2810%2C%281.0001096%29%29=365%2At\" Divide both sides by \"log%2810%2C%281.0001096%29%29\".\r
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\n" ); document.write( "\n" ); document.write( "\"2036.0928773=365%2At\" Evaluate the left side with a calculator.\r
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\n" ); document.write( "\n" ); document.write( "\"2036.0928773%2F365=t\" Divide both sides by \"365\" to isolate 't'.\r
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\n" ); document.write( "\n" ); document.write( "\"5.5783367=t\" Divide.\r
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\n" ); document.write( "\n" ); document.write( "\"t=5.5783367\" Rearrange the equation.\r
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\n" ); document.write( "\n" ); document.write( "\"t=5.58\" Round to the nearest hundredth.\r
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\n" ); document.write( "\n" ); document.write( "So it will take about 5.58 years for an initial investment of $40 to grow to $50 (compounded 365 times a year at 4%).
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