document.write( "Question 1137034: At age 25, to save for retirement, you decide to deposit $75.00 into an IRA at the end of each month, at an interest rate of 6.5% PER YEAR COMPOUNDED DAILY. How much will you have from the IRA when you retire at age 65? \n" ); document.write( "

Algebra.Com's Answer #754871 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "It works very similar to Ordinary Annuity saving plan.\r\n" );
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document.write( "But since the deposit periods and compounding periods are different, it requires some modifications.\r\n" );
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document.write( "I will explain which modifications are needed. \r\n" );
document.write( "In my solution, I will assume that each month is 30 days (so one/each year is 360 days).\r\n" );
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document.write( "You deposit P = 75 dollars at the end of each month. This amount of 75 dollars is compounded daily next month\r\n" );
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document.write( "according to the formula \r\n" );
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document.write( "            F = \r\n" );
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document.write( "and becomes\r\n" );
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document.write( "            F = 75.40732 dollars.\r\n" );
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document.write( "I could round it to cents, but do not want to do it now.\r\n" );
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document.write( "Also, the monthly growing factor is  \r\n" );
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document.write( "            G =  = 1.005431.\r\n" );
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document.write( "and it shows that the standard \"r\" of the Ordinary Annuity saving plan is r= 0.005431, considered for monthly compounding.\r\n" );
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document.write( "So, the process works in a way as if you deposit not $75.00, but 75.40732 dollars at the end of each month,\r\n" );
document.write( "and if the account is compounded NOT DAILY, but MONTHLY with the monthly value of r equal to  0.005431.\r\n" );
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document.write( "After making this notice, you just apply the standard formula for the Ordinary Annuity saving plan, assuming \r\n" );
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document.write( "    monthly payment is 75.40732 dollars deposited at the end of each month;\r\n" );
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document.write( "    compounding period is ONE MONTH;   and\r\n" );
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document.write( "    the number of compounding periods is 12*40.\r\n" );
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document.write( "So, apply now the standard Ordinary Annuity saving plan formula\r\n" );
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document.write( "    Future value =  =  = 173,021.73 dollars.    ANSWER\r\n" );
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\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
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\n" ); document.write( "\n" ); document.write( "The lessons contain EVERYTHING you need to know about the classic Ordinary Annuity saving plan, in clear and compact form.\r
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