document.write( "Question 1201177: The present value of a sum of money is the amount that must be invested now, at a given rate of interest, to produce the desired sum at a later date.\r
\n" ); document.write( "\n" ); document.write( "Find the present value of $10,000 if interest is paid at a rate of 6% per year, compounded semiannually, for 5 years. (Round your answer up to the next cent.) \n" ); document.write( "

Algebra.Com's Answer #835441 by Theo(13342) $\"\"$ $\"About$

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the amount is 10,000 and it is presumably available in 5 years.
\n" ); document.write( "the present value at 6% per year, compounded semi-annually is:
\n" ); document.write( "p = 10,000 / ((1 + .6/2) ^ (5*2))
\n" ); document.write( "this becomes:
\n" ); document.write( "p = 10,000 / (1.03 ^ 10).
\n" ); document.write( "solve for p (stands for present value) to get:
\n" ); document.write( "p = 7,440.939149.
\n" ); document.write( "that's how much you woud have to invest today so you can have 10,000 in 5 years.
\n" ); document.write( "since the annual interest rate is compounded semi-annually, then you need to find the interest rate per semi-annual period.
\n" ); document.write( "that is equal to .06/2 = .05
\n" ); document.write( "the number of time periods is 5 years * 2 semi-annual periods per year = 10 semi-annual time period.
\n" ); document.write( "take 7440.939149 and multiply it by 1.03 ^ 10 and you will get 10,000.\r
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