document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201131>Question 1201131</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Formulate a system of equations for the situation below and solve.<BR>\n" );
document.write( "A private investment club has $400,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low-risk. Management estimates that high-risk stocks will have a rate of return of 15%/year; medium-risk stocks, 10%/year; and low-risk stocks, 6%/year. The members have decided that the investment in low-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $40,000/year on the total investment. (Assume that all the money available for investment is invested.)<BR>\n" );
document.write( "high-risk stocks	$ <BR>\n" );
document.write( "medium-risk stocks	$ <BR>\n" );
document.write( "low-risk stocks	$ </SPAN>\n" );
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document.write( "The problem requires that half of the $400,000 be invested in the low-risk stocks that yield a return of 6%.  $200,000 invested at 6% yields .06($200000) = $12,000.<br><BR>\n" );
document.write( "The total return required is $40,000, so the $200,000 invested in the stocks that have returns of 10% and 15% must yield a return of $40,000-$12,000 = $28,000.<br><BR>\n" );
document.write( "A yield of $28,000 on an investment of $200,000 requires an average interest rate of $28,000/$200,000 = 0.14 = 14%.<br><BR>\n" );
document.write( "Simple mental arithmetic shows that 14% is four-fifths of the way from 10% to 15%; that means 4/5 of the remaining $200,000, or $160,000, must be invested at the higher rate.<br><BR>\n" );
document.write( "ANSWER:<BR>\n" );
document.write( "$160,000 at 15%<BR>\n" );
document.write( "$40,000 at 10%<BR>\n" );
document.write( "$200,000 at 6%<br><BR>\n" );
document.write( "CHECK: .15($160,000) + .10($40,000) + .06($200,000) = $24,000 + $4000 + $12,000 = $40,000<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );