document.write( "Question 1201794: You put $159 per month in an investment plan that pays an APR of 5%. How much money will you have after 24 years? Compare this amount to the total amount of deposits made over the time period. \n" ); document.write( "
Algebra.Com's Answer #836335 by ikleyn(52932)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "You put $159 per month in an investment plan that pays an APR of 5%.
\n" ); document.write( "How much money will you have after 24 years?
\n" ); document.write( "Compare this amount to the total amount of deposits made over the time period.
\n" ); document.write( "~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        This problem is posed in a strange way, unprofessionally.\r
\n" ); document.write( "\n" ); document.write( "        To be professional, the problem should say whether the regular monthly payments \r
\n" ); document.write( "\n" ); document.write( "        are made: at the beginning of each month or at the end of each month.\r
\n" ); document.write( "\n" ); document.write( "        Computational procedures are different in these cases, and the answers are different, too.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        In my solution, I will assume that the regular monthly payments of $159
\n" ); document.write( "        are made at the end of each month (ordinary annuity).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "Then it is a classic Ordinary Annuity saving plan. The general formula is \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    FV = \"P%2A%28%28%281%2Br%29%5En-1%29%2Fr%29\",    (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "where  FV is the future value of the account;  P is your monthly payment (deposit); \r\n" );
document.write( "r is the monthly percentage yield presented as a decimal; \r\n" );
document.write( "n is the number of deposits (= the number of years multiplied by 12, in this case).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Under the given conditions, P = 159;  r = 0.05/12;  n = 12*24 = 288.  \r\n" );
document.write( "So, according to the formula (1), you get at the end of the 24-th year\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    FV = \"159%2A%28%28%281%2B0.05%2F12%29%5E288-1%29%2F%28%280.05%2F12%29%29%29\" =  $88,220.19.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Note that you the deposited amount is only  12*24*159 = $45,792.  The rest is what the account earns/accumulates in 24 years.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "-----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "On Ordinary Annuity saving plans,  see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Ordinary Annuity saving plans and geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on Ordinary Annuity saving plans\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The lessons contain  EVERYTHING  you need to know about this subject,  in clear and compact form.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "When you learn from these lessons,  you will be able to do similar calculations in semi-automatic mode.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );