Algebra.Com's Answer #851926 by ikleyn(52785)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
.
\n" );
document.write( "Grandma decides to put 1300 dollars every month into an account for you. She makes 23 monthly deposits,
\n" );
document.write( "the last coming September 1, 2003 - the day you start college. She wants you to be able to withdraw money
\n" );
document.write( "from this account at the beginning of each month, with the first withdrawal coming September 1, 2003
\n" );
document.write( "and the last coming June 1, 2008, (when you'll graduate). (Note: that makes 58 withdrawals total.)
\n" );
document.write( "How much will you be able to withdraw each month if the account is earning a nominal interest rate
\n" );
document.write( "of 9.3 percent convertible monthly?
\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( " The problem uses the term \" convertible \" instead of \" compounded \".\r
\n" );
document.write( "\n" );
document.write( " This term \" convertible \" is NEVER USED in this context.\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( " I performed all calculations accurately in a way as it SHOULD be done.\r
\n" );
document.write( "\n" );
document.write( " My numbers and my answer are different from that by @CPhill.\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "\r\n" );
document.write( "Let's break this problem into two parts:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "**Part 1: Calculate the Accumulated Value of Grandma's Deposits**\r\n" );
document.write( "\r\n" );
document.write( "1. **Monthly Deposit:** $1300\r\n" );
document.write( "2. **Number of Deposits:** 23\r\n" );
document.write( "3. **Interest Rate:** 9.3% compounded monthly (effective rate r = 0.093/12 per month)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We'll use the future value of an ordinary annuity formula:\r\n" );
document.write( "\r\n" );
document.write( " FV =  , (1)\r\n" );
document.write( "\r\n" );
document.write( "where\r\n" );
document.write( "\r\n" );
document.write( "* FV = Future Value\r\n" );
document.write( "* P = Periodic Payment ($1300)\r\n" );
document.write( "* r = Interest Rate per Period (0.00775)\r\n" );
document.write( "* n = Number of Periods (23)\r\n" );
document.write( "\r\n" );
document.write( " FV =  (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "I used MS Excel software in my computer.\r\n" );
document.write( "It is commonly considered as an appropriate tool for such calculations, \r\n" );
document.write( "since it provides the necessary precision.\r\n" );
document.write( "I copied and pasted this formula into a MS Excel, and I got the value of $32,592.78.\r\n" );
document.write( "\r\n" );
document.write( "I did not make intermediate rounding, since intermediate rounding are PROHIBITED \r\n" );
document.write( "in such calculation: they influence to the final result and lead to wrong answer.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " I checked this value using an online calculator at this web-site\r\n" );
document.write( "\r\n" );
document.write( " https://www.omnicalculator.com/finance/annuity-future-value\r\n" );
document.write( "\r\n" );
document.write( " https://www.omnicalculator.com/finance/annuity-future-value\r\n" );
document.write( "\r\n" );
document.write( " I got precisely the same dollars and precisely the same cents.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "**Part 2: Calculate the Monthly Withdrawal Amount**\r\n" );
document.write( "\r\n" );
document.write( "1. **Accumulated Value (Present Value for Withdrawals):** $32592.78\r\n" );
document.write( "2. **Number of Withdrawals:** 58\r\n" );
document.write( "3. **Interest Rate:** 9.3% monthly (effective compounding rate r = 0.093/12 per month)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We'll use the present value of an annuity due formula since withdrawals are at the beginning of each month:\r\n" );
document.write( "\r\n" );
document.write( " PV =  , (3)\r\n" );
document.write( "\r\n" );
document.write( "where:\r\n" );
document.write( "\r\n" );
document.write( "* PV = Present Value ($32592.78)\r\n" );
document.write( "* M = Monthly Withdrawal Amount\r\n" );
document.write( "* r = Interest Rate per Period (0.093/12)\r\n" );
document.write( "* n = Number of Periods (58)\r\n" );
document.write( "\r\n" );
document.write( "Rearrange the formula (3) to solve for M:\r\n" );
document.write( "\r\n" );
document.write( " M =  , (4)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " M =  . (5)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Again, I used MS Excel software in my computer.\r\n" );
document.write( "It is commonly considered as an appropriate tool for such calculations, \r\n" );
document.write( "since it provides the necessary precision.\r\n" );
document.write( "I copied and pasted this formula into a MS Excel, and I got the value of $694.43.\r\n" );
document.write( "\r\n" );
document.write( "I did not make intermediate rounding, since intermediate rounding are PROHIBITED \r\n" );
document.write( "in such calculation: they influence to the final result and lead to wrong answer.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer. You will be able to withdraw approximately $694.43 at the beginning of each month.\r\n" );
document.write( " \r
\n" );
document.write( "\n" );
document.write( "Solved.\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( "Dear @CPhill,\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "I want you do understand me correctly.\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "After all, in real life it does not matter, if you make a mistake in 10 cents or even in one dollar.\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "But if you are an \" Artificial Intelligence \", you have no right to make a computational mistake even in one cent.\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "You either use a commonly accepted, trusted, proven computing methodology, \r
\n" );
document.write( "\n" );
document.write( "or, as an alternative, NOBODY and NEVER will trust you.\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( " \n" );
document.write( " |