document.write( "Question 1196114: You currently have $8,800 (Present Value) in an account that has an interest rate of 6% per year compounded daily (365 times per year). You want to withdraw all your money when it reaches $16,720 (Future Value). In how many years will you be able to withdraw all your money? \n" ); document.write( "

Algebra.Com's Answer #828821 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "You currently have $8,800 (Present Value) in an account that has an interest rate
\n" ); document.write( "of 6% per year compounded daily (365 times per year). You want to withdraw all your
\n" ); document.write( "money when it reaches $16,720 (Future Value). In how many years will you be able
\n" ); document.write( "to withdraw all your money?
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document.write( "Let \"r\" be the compound interest rate per annum.\r\n" );
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document.write( "Start from the formula for the future value\r\n" );
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document.write( "    16720 = ,\r\n" );
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document.write( "where \"n\" is the number of days.\r\n" );
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document.write( "It is the same as\r\n" );
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document.write( "     = ,\r\n" );
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document.write( "or\r\n" );
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document.write( "    1.9 = .\r\n" );
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document.write( "Take logarithm base 10 of both sides of the equation\r\n" );
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document.write( "    log(1.9) = n*log(1.000164384).\r\n" );
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document.write( "Find  n =  = 3904.92 days, or 3905 days, rounded to the closest greater number of days.\r\n" );
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document.write( "3905 days = 10 years 8 months and about 12 days  (counting 365 days/year, 30 days per month).\r\n" );
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document.write( "ANSWER. The time to wait is 3905 days, or 10 years, 8 months and about 12 days.\r\n" );
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