document.write( "Question 1198072: 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 10% per year, compounded semiannually, for 2 years. (Round your answer up to the next cent.)
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #831596 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "The present value of a sum of money is the amount that must be invested now,
\n" ); document.write( "at a given rate of interest, to produce the desired sum at a later date.
\n" ); document.write( "Find the present value of $10,000 if interest is paid at a rate of 10% per year,
\n" ); document.write( "compounded semiannually, for 2 years. (Round your answer up to the next cent.)
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "desired value = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " = 1.05  is the effective growth rate per half of a year.\r\n" );
document.write( "\r\n" );
document.write( "The 2*2 in the power is 2 halves of a year taken twice, for two years.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus, the equation is\r\n" );
document.write( "\r\n" );
document.write( "    10000 =  \r\n" );
document.write( "\r\n" );
document.write( "or\r\n" );
document.write( "\r\n" );
document.write( "    10000 = ,\r\n" );
document.write( "\r\n" );
document.write( "which gives\r\n" );
document.write( "\r\n" );
document.write( "    present value =  = 8227.024748 = 8227.03 dollars, rounded up to the nearest cent.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );