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%.

Answer 1

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)

Answer 2

To set up a trust fund for her two children, Deborah needs to determine the investment allocation between the bond fund and the stock fund. She wants to ensure that she invests at least 30% in the bond fund and achieve a total return of at least 7.5%.

Let's assume Deborah decides to invest a total amount X in the trust fund. Given her preference for at least 30% in the bond fund, she will allocate at least 0.3X to the bond fund.

To calculate the minimum amount to allocate to the stock fund, we subtract the amount allocated to the bond fund from the total investment amount: X - 0.3X = 0.7X.

To achieve a total return of at least 7.5%, Deborah needs to consider the individual returns of the bond and stock funds. The total return will be the weighted average of the returns of each investment, based on the allocation.

Let's represent the return percentage of the bond fund as R_bond and the return percentage of the stock fund as R_stock. Given that the projected returns are 6% for the bond fund and 10% for the stock fund:

(R_bond * 0.3X + R_stock * 0.7X) / X ≥ 7.5

Simplifying the equation:

0.3 * R_bond + 0.7 * R_stock ≥ 7.5

Now we can solve this inequality to find the minimum required return for the stock fund.

0.7 * R_stock ≥ 7.5 - 0.3 * R_bond

R_stock ≥ (7.5 - 0.3 * R_bond) / 0.7

So, the minimum return required for the stock fund is (7.5 - 0.3 * R_bond) / 0.7.

By setting the allocation to the bond fund at 30%, we can now calculate the required minimum return for the stock fund.