document.write( "Question 1158170: lee deposits $200 every month into a savings account that earns 3.25% compounded monthly. how many years would it take lee to reach his savings goal of $9000. keep 2 decimal places in your final anwser. \n" ); document.write( "

Algebra.Com's Answer #853716 by ikleyn(53618) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Lee deposits $200 every month into a savings account that earns 3.25% compounded monthly.
\n" ); document.write( "How many years would it take lee to reach his savings goal of $9000. keep 2 decimal places in your final anwser.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        First, I will solve this problem.\r
\n" ); document.write( "\n" ); document.write( "        After finishing my solution, I will discuss on how the problem is posed, worded, \r
\n" ); document.write( "\n" ); document.write( "        and what I think about all of this.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Use a standard formula for the future value of an ordinary annuity compounded  monthly\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    FV = \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "where FV is the future value, P is the payment at the end of each month, \r\n" );
document.write( "r is the nominal interest rate per year expressed as decimal, \r\n" );
document.write( "n is the number of monthly deposits (of months).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, we need to find \" n \" from this equation\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     =  =  = 45, \r\n" );
document.write( "\r\n" );
document.write( "     = . \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Rewrite it in this form\r\n" );
document.write( "\r\n" );
document.write( "     = 0.121875,\r\n" );
document.write( "\r\n" );
document.write( "     = 1 + 0.121875 = 1.121875.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Take logarithm base 10 of both sides\r\n" );
document.write( "\r\n" );
document.write( "    n*log(1+0.0325/12) = log(1.121875)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "and calculate  \r\n" );
document.write( "\r\n" );
document.write( "     n =  = 42.51952746 months.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now we should round it to the closest greater integer number of months, which is 43 months,\r\n" );
document.write( "in order for the bank would be in position to perform the last compounding at the end of the 43-th month.\r\n" );
document.write( "43 months is the same as 3 years and 7 months.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The amount will exceed the goal of $9,000 in 43 months, or 3 years and 7 months.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The instruction to this problem, saying \" keep 2 decimal places in your final answer \", is incorrect and non-sensical.
\n" ); document.write( "The answer to this problem should be expressed as an integer number of months.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since the instruction is incorrect and non-sensical, it tells me that a person who created this problem,
\n" ); document.write( "is (1) unprofessional Math writer/composer and (2) is a random person in this field.
\n" ); document.write( "He or she is still able to re-write from other sources, but does not understand the meaning of the problem
\n" ); document.write( "and does not really understand what he/she writes or re-writes. It is very sad to me to see it and to tell it.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I have been solving problems on this forum for many years.
\n" ); document.write( "I've seen dozens similar problems like
\n" ); document.write( "\"how long does it take for a discretely compounded account to get an assigned value\".
\n" ); document.write( "and I myself have probably solved about fifteen such problems at this forum.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " But I have never seen such a problem formulated correctly at the forum.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "They always asked for a final result \"with two decimal places,\" which is meaningless in such problems,
\n" ); document.write( "where the final answer MUST be expressed in integer number of compounding periods.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Okay, I know, and you don't need to explain or refute it to me, that most of the incoming tasks
\n" ); document.write( "are intended for use as solutions on other websites or as a knowledge base for artificial intelligence.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "But then, dear managers, you must ensure that you employ the most highly qualified people in the field.
\n" ); document.write( "However, what I see in the example of this task tells me the opposite - some of your employees do not meet
\n" ); document.write( "the high standards required for creating artificial intelligence.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "And this is not just anywhere, but in the crucial matter of correctly formulating
\n" ); document.write( "the problem statement, where everything must be perfectly smooth and accurate.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );