Deborah inherited a large sum of money; she wants to use a portion of this money to set up a trust fund for her two children. The trust fund has two investment options: 1) a bond fund and 2) a stock fund. The projected returns over the life of the investments are 6% for the bond fund and 10% for the stock fund. Whatever portion of the inheritance she finally decides to commit to the trust fund, she wants to invest at least 30% of the amount in the bond fund. In addition, she wants to select a mix that will enable her to obtain a total return of at least 7.5%.

Question

Deborah inherited a large sum of money; she wants to use a portion of this money to set up a trust fund for her two children.  The trust fund has two investment options: 1) a bond fund and 2) a stock fund.  The projected returns over the life of the investments are 6% for the bond fund and 10% for the stock fund.  Whatever portion of the inheritance she finally decides to commit to the trust fund, she wants to invest at least 30% of the amount in the bond fund.  In addition, she wants to select a mix that will enable her to obtain a total return of at least 7.5%.

MathMate · Answer

Let
b=fraction of investments for bonds,
1-b=fraction of investments for stocks.
we require b>0.3:
Thus
b*0.06+(1-b)*0.1=0.075

Solve the equation for the maximum value of b. Also make sure that b>0.3,
(answer is 0.3≤ b ≤5/8)