document.write( "Question 1157223: A person plans to invest a total of $80,000 in a money market account, a bond fund, an international stock fund, and a domestic stock fund. She wants 60% of her investment to be conservative (money market and bonds). She wants the amount in domestic stocks to be 4 times the amount in international stocks. Finally, she needs an annual return of $3,200. Assuming she gets annual returns of 2.5% on the money market account, 3.5% on the bond fund, 4% on the international stock fund, and 6% on the domestic stock fund, how much should she put in each investment? \n" ); document.write( "

Algebra.Com's Answer #780054 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "According to the condition, 60% of $80000, i.e. 0.6*80000 = 48000 dollars go to \r\n" );
document.write( "the money market and a bond account.\r\n" );
document.write( "\r\n" );
document.write( "The rest, $80000 - $48000 = $32000 go the the international stock fund and domestic stock fund.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let x be the amount to invest to the international stock fund; then the amount going\r\n" );
document.write( "to the domestic stock fund is 4x dollars, according to the condition.\r\n" );
document.write( "\r\n" );
document.write( "So, our first equation is\r\n" );
document.write( "\r\n" );
document.write( "    x + 4x = 32000\r\n" );
document.write( "\r\n" );
document.write( "giving  \r\n" );
document.write( "\r\n" );
document.write( "    5x = 32000,\r\n" );
document.write( "\r\n" );
document.write( "     x = 32000/5 = 6400.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus $6400 go to the international stock fund and 4*6400 = 25600 dollars go to the domestic stock fund.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "These two investments produce  the annual interest of 0.04*6400 + 0.066*25600 = 1792 dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence, we should get the rest  annual return of 3200-1792 = 1408 from two other funds, the money market account and the bond fund.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let y be the amount to invest to bond fund.\r\n" );
document.write( "\r\n" );
document.write( "Then the amount to invest to the money market account is  48000-y.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We then have this equation\r\n" );
document.write( "\r\n" );
document.write( "    0.035y + 0.025(48000-y) = 1408.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From the equation,\r\n" );
document.write( "\r\n" );
document.write( "    y =  = 20800.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus $20800 goes to the bond fund, and the rest 48000-20800 = 27200 dollars go to the market account.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  $27200 to the narket account;  $20800 to the bond fund;  $25600 to the domestic stock and $6400 to the international stock fund.\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" );