document.write( "Question 612375: In how many years will an account double itself at 5% interest compounded annually \n" ); document.write( "
Algebra.Com's Answer #385406 by Edwin McCravy(20055)\"\" \"About 
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In how many years will an account double itself at 5% interest compounded annually
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document.write( "Use the formula\r\n" );
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document.write( "A = P(1 + \"r%2Fn\")nt\r\n" );
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document.write( "Where \r\n" );
document.write( "A = the final amount\r\n" );
document.write( "P = the beginning amount\r\n" );
document.write( "r = the annual rate expressed as a decimal\r\n" );
document.write( "n = the number of times per year interest is compunded\r\n" );
document.write( "t = the number of years invested\r\n" );
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document.write( "In the case the interest is compounded 1 time per year,\r\n" );
document.write( "so the n's are just 1 and we can write the formula as\r\n" );
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document.write( "A = P(1 + r)t \r\n" );
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document.write( "We want to find t when the final amount A is twice the beginning\r\n" );
document.write( "amount P.  So we substitute 2P for A, and .05 for r\r\n" );
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document.write( "2P = P(1 + .05)t\r\n" );
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document.write( "2P = P(1.05)t\r\n" );
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document.write( "We divide both sides by P and get\r\n" );
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document.write( "2 = (1.05)t\r\n" );
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document.write( "We lake logs of both sides:\r\n" );
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document.write( "log(2) = log(1.05)t\r\n" );
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document.write( "Then we use a rule of logarithms which allows us to\r\n" );
document.write( "write the exponent t as a coefficient of the log:\r\n" );
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document.write( " log(2) = t·log(1.05}\r\n" );
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document.write( "We divide both sides by log(1.05)\r\n" );
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document.write( "\"log%28%282%29%29%2Flog%28%281.05%29%29\" = t\r\n" );
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document.write( "Use a calculator to get the left side:\r\n" );
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document.write( "14.20669908 = t\r\n" );
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document.write( "It will not quite be doubled after 14 years, but it will be\r\n" );
document.write( "more than doubled after 15 years.\r\n" );
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document.write( "Edwin
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