document.write( "Question 923755: I have been pounding my head for 2 days trying to figure out the right equation for this problem and I am hoping someone here can help.
\n" ); document.write( "What is the amount a person would have to deposit today to be able to take out $5000 a year for 10 years from an account earning 8 percent annually?
\n" ); document.write( "Thanks! \n" ); document.write( "

Algebra.Com's Answer #560304 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
The way I understand it you want to know how much money should be deposited at time = 0 years,
\n" ); document.write( "into an account earning 8 percent annually,
\n" ); document.write( "so that at t=1 year, t=2 years, ..., t=8 years,
\n" ); document.write( "there would be at least $5000 that can be taken out.
\n" ); document.write( "At $\"t=0\"$ , $\"balance%5B0%5D+=+A\"$ .
\n" ); document.write( "At $\"t=1\"$ (at the end of the first year) 8% interest ( $\"0.08A\"$ is added to the balance,
\n" ); document.write( "bringing the balance up to $\"A%2B0.08A=1.08A\"$ ,
\n" ); document.write( "and immediately, $\"5000\"$ is taken out,
\n" ); document.write( "bringing the balance down to $\"balance%5B1%5D=1.08A-5000\"$
\n" ); document.write( "At $\"t=2\"$ , $\"balance%5B1%5D\"$ is again
\n" ); document.write( "increased by a factor of $\"1.08\"$ ,
\n" ); document.write( "and reduced by the withdrawal of $\"5000\"$ , so
\n" ); document.write( "

.
\n" ); document.write( "At $\"t=3\"$ , $\"balance%5B2%5D\"$ is again
\n" ); document.write( "increased by a factor of $\"1.08\"$ ,
\n" ); document.write( "and reduced by the withdrawal of $\"5000\"$ , so
\n" ); document.write( "

.
\n" ); document.write( "This pattern repeats every year, and
\n" ); document.write( "at $\"t=10\"$ ,
\n" ); document.write( "

\n" ); document.write( "If at that point $\"balance%5B10%5D=0\"$ ,
\n" ); document.write( "

\n" ); document.write( " $\"A%2A1.08%5E10=5000%2A%28%281.08%5E10-1%29%2F%281.08-1%29%29\"$
\n" ); document.write( " $\"A%2A1.08%5E10=5000%2A%28%281.08%5E10-1%29%2F0.08%29\"$
\n" ); document.write( " $\"A=5000%2A%281.08%5E10-1%29%2F%280.08%2A1.08%5E10%29\"$
\n" ); document.write( " $\"A=28733.19\"$
\n" ); document.write( "
\n" ); document.write( "NOTE:
\n" ); document.write( "The sum $\"SUM=1.08%5E9%2B1.08%5E8%2B1.08%5E7%2B+%22...%22+%2B1.08%5E2%2B1.08%2B1\"$
\n" ); document.write( "is the sum of a geometric sequence with ratio $\"1.08\"$ .
\n" ); document.write( "You may know a formula for that, but otherwise you can see that
\n" ); document.write( " $\"1.08%2ASUM=1.08%5E10%2B1.08%5E9%2B1.08%5E8%2B1.08%5E7%2B+%22...%22+%2B1.08%5E2%2B1.08\"$ , and then
\n" ); document.write( " $\"1.08%2ASUM-SUM=1.08%5E10-1\"$ ---> $\"%281.08-1%29%2ASUM=1.08%5E10-1\"$ ---> $\"SUM=%281.08%5E10-1%29%2F%281.08-1%29\"$ \n" ); document.write( "

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