document.write( "Question 1204090: You currently have $6,500 (Present Value) in an account that has an interest rate of 7% per year compounded monthly (12 times per year). You want to withdraw all your money when it reaches $16,250 (Future Value). In how many years will you be able to withdraw all your money? Round your answer to 1 decimal place. \n" ); document.write( "

Algebra.Com's Answer #840109 by ikleyn(52802) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "        If you discard all the verbal husk, then the standard question remains: \r
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\n" ); document.write( "\n" ); document.write( "            How long will it take for the deposit of $6500 to get the value of $16,250,
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document.write( "Use the formula for the future value of this compounded account\r\n" );
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document.write( "    16250 = ,\r\n" );
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document.write( "where n is the number of months.\r\n" );
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document.write( "Solve this equation to find n, step by step\r\n" );
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document.write( "     = ,\r\n" );
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document.write( "    2.5 = .\r\n" );
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document.write( "Take logarithm base 10 of both sides\r\n" );
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document.write( "    log(2.5) = n*log(1.005833333)\r\n" );
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document.write( "Find n =  = 157.54 months.\r\n" );
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document.write( "Round to the closest  month, in order for the bank was in position\r\n" );
document.write( "to make the last compounding.\r\n" );
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document.write( "ANSWER.  158 months, or  13 years and 2 months.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Notice that in this problem, the answer in decimals is NOT ACCEPTABLE.\r
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\n" ); document.write( "\n" ); document.write( "The answer must be in months, because the month is THE DISCRETE TIME UNIT
\n" ); document.write( "for this problem / (for such problems), due to compounding.\r
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\n" ); document.write( "\n" ); document.write( "Solving problems for discretely compounded accounts, it is important to understand these things:\r
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\n" ); document.write( "\n" ); document.write( "(1)   The continuous time IS NOT USED and SHOULD NOT be used in the solution,
\n" ); document.write( "         since the compounding amount IS NOT a continuous function.\r
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\n" ); document.write( "\n" ); document.write( "         The compounded account changes by jumping at the end of each compound period.\r
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\n" ); document.write( "\n" ); document.write( "(2)   The answer must be in integer number of compounding periods;\r
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\n" ); document.write( "\n" ); document.write( "(3)   Your goal is not to get precisely the assigned amount - $\"highlight%28highlight%28NO%29%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "        Your goal is to find the first discrete time, when the compounded account will exceed the assigned amount.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar (and different) solved problems, look into the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Problems on discretely compound accounts \r
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\n" ); document.write( "\n" ); document.write( "After reading this lesson, you will tackle such problems on your own without asking for help from outside.\r
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