document.write( "Question 1201799: M wishes to determine how long it will take an initial deposit of $10,000 to double.
\n" ); document.write( "Required:
\n" ); document.write( "a) If M earns 10% annual interest on the deposit, how long will it take for him to double his money?
\n" ); document.write( "b) How long will it take if he earns only 7% annual interest?
\n" ); document.write( "c) Reviewing your findings in parts a and b, indicate what relationship exists between the interest rate and the amount of time it will take M to double his money.
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #836303 by ikleyn(52814)\"\" \"About 
You can put this solution on YOUR website!
M wishes to determine how long it will take an initial deposit of $10,000 to double.
\n" ); document.write( "Required:
\n" ); document.write( "a) If M earns 10% annual interest on the deposit, how long will it take for him to double his money?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "For the amount of $10,000, compounded yearly, the future value formula is\r\n" );
document.write( "\r\n" );
document.write( "    Future Value = \"10000%2A%281%2B0.1%29%5En\"\r\n" );
document.write( "\r\n" );
document.write( "where n is the number of years.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore, our equation to find \"n\" is\r\n" );
document.write( "\r\n" );
document.write( "    20000 = \"10000%2A1.1%5En\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by 10000\r\n" );
document.write( "\r\n" );
document.write( "    \"20000%2F10000\" = \"1.1%5En\",\r\n" );
document.write( "\r\n" );
document.write( "or, reducing left side,\r\n" );
document.write( "\r\n" );
document.write( "    2 = \"1.1%5En\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To solve this equation, take logarithm base 10 of both sides\r\n" );
document.write( "\r\n" );
document.write( "    log(2) = n*log(1.1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "and find \"n\" using your calculator\r\n" );
document.write( "\r\n" );
document.write( "    n = \"log%28%282%29%29%2Flog%28%281.1%29%29\" = 7.27  years.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Finally, round this value 7.27 to the nearest greater integer 8 (8 years),\r\n" );
document.write( "\r\n" );
document.write( "in order for the bank was in position to make the last compounding.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER. 8 years.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Do other part similarly: continue by the same way.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------------\r
\n" ); document.write( "
\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
\n" ); document.write( "\n" ); document.write( "in this site,  and learn the subject from there.\r
\n" ); document.write( "
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Happy learning (!)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "///////////////////\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Hello, when you see the answer from other tutor/tutors to this problem,
\n" ); document.write( "not rounded to the whole  (integer)  number of years,  this answer  (or such answer)  is  INCORRECT.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The problem  ASSUMES  that you round the decimal number of years to the closest greater  INTEGER  number of years.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Any reasonable person,  solving such problems,  should understand it as clear
\n" ); document.write( "as he  (or she)  does understand that   2 x 2  is  4.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );