document.write( "Question 1201478: Please help me with this problem. Would greatly appreciate your help!\r
\n" ); document.write( "\n" ); document.write( "You win the lottery and get $100 per day for 25 years. Assuming a yearly interest rate of 6%, compounded daily, how much is the series of payments worth in today's dollars? \n" ); document.write( "
Algebra.Com's Answer #835869 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "You win the lottery and get $100 per day for 25 years.
\n" ); document.write( "Assuming a yearly interest rate of 6%, compounded daily,
\n" ); document.write( "how much is the series of payments worth in today's dollars?
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document.write( "This saving plan of depositing $100 per day for 25 years at a yearly interest rate of 6%, \r\n" );
document.write( "compounded daily, is called an ORDINARY ANNUITY plan.\r\n" );
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document.write( "There is a formula to calculate the total amount which the plan generate at the end.\r\n" );
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document.write( "This formula is\r\n" );
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document.write( "    f = \"p+%2A+%28%28%281+%2B+r%29+%5E+n-1%29%2Fr%29\",\r\n" );
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document.write( "f is the future value\r\n" );
document.write( "p is the daily payment\r\n" );
document.write( "r is the interest rate per time period\r\n" );
document.write( "n is the number of time periods.\r\n" );
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document.write( "In your problem:\r\n" );
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document.write( "time periods are days.\r\n" );
document.write( "p = 100 dollars  \r\n" );
document.write( "r = 0.06/365 per day (counting 365 days in a year)\r\n" );
document.write( "n = 25*365 = 9125 days in 25 years\r\n" );
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document.write( "formula becomes f = \"100%2A%28%28%281+%2B+0.06%2F365%29%5E9125-1%29%2F%28%280.06%2F365%29%29%29\" = 2,117,691.45 dollars (rounded).\r\n" );
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document.write( "Now, your problem asks, what amount should be deposited one time today\r\n" );
document.write( "on the 25 years account giving 6% interest rate annually and compounded daily,\r\n" );
document.write( "in order for to get the same total of $2,117,691.45 at the end of 25 years?\r\n" );
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document.write( "To determine it, we write this equation for the unknown principal amount P\r\n" );
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document.write( "    2117691.45 = \"P%2A%281%2B0.06%2F365%29%5E9125\".\r\n" );
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document.write( "From this equation we get the ANSWER\r\n" );
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document.write( "    P = \"2117691.45%2F%281%2B0.06%2F365%29%5E9125\" = 472579.09.\r\n" );
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document.write( "So, in today's dollars, your winning is EQUIVALENT to  $472,579.09.    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
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\n" ); document.write( "\n" ); document.write( "The lessons contain  EVERYTHING  you need to know about this subject,  in clear and compact form.\r
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\n" ); document.write( "\n" ); document.write( "On discretely compounded accounts,  see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Compound interest percentage problems \r
\n" ); document.write( "\n" ); document.write( "    - Problems on discretely compound accounts \r
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