document.write( "Question 368594: You make a deposit of 2000€ into your account. the interest rate is 5% and the interest is added into the account first after one year and then annually. how long will it take your savings to grow to 10000€ ? \n" ); document.write( "
Algebra.Com's Answer #262653 by Edwin McCravy(20056)\"\" \"About 
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You make a deposit of 2000€ into your account. the interest rate is 5% and the interest is added into the account first after one year and then annually. how long will it take your savings to grow to 10000€ ?
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document.write( "\"A+=+P%281%2Br%2Fn%29%5E%28nt%29\"\r\n" );
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document.write( "A = Final amount                 = 10000€\r\n" );
document.write( "P = Beginning amount             = 2000€\r\n" );
document.write( "r = rate expressed as a decimal  = .05\r\n" );
document.write( "n = number of compounding/year   = 1 since it is annually (1 time per year)\r\n" );
document.write( "t = time in years                = what we are to find out.\r\n" );
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document.write( "Substituting:\r\n" );
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document.write( "\"A+=+P%281%2Br%2Fn%29%5E%28nt%29\"\r\n" );
document.write( "\"10000+=+2000%281%2B.05%2F1%29%5E%28%281%29t%29\"\r\n" );
document.write( "\"10000+=+2000%281%2B.05%29%5Et\"\r\n" );
document.write( "\"10000+=+2000%281.05%29%5Et\"\r\n" );
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document.write( "Divide through by 2000\r\n" );
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document.write( "\"5+=+1.05%5Et\"\r\n" );
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document.write( "Take logarithms (base 10) of both sides:\r\n" );
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document.write( "\"log%285%29+=+log%281.05%5Et%29\"\r\n" );
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document.write( "Use the rule of logarithms:  \"log%28B%5EA%29+=+A%2Alog%28B%29\"\r\n" );
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document.write( "\"log%285%29+=+t%2Alog%281.05%29\"\r\n" );
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document.write( "Divide both sides by \"log%281.05%29\"\r\n" );
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document.write( "\"log%285%29%2Flog%281.05%29+=+t\"\r\n" );
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document.write( "Use a calculator:\r\n" );
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document.write( "\"32.98693374\"\r\n" );
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document.write( "Answer: 33 years.\r\n" );
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document.write( "Edwin
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