Question

The parents of three children, ages 1, 3, and 6, wish to set up a trust fund that will pay X to each child upon attainment of age 18, and Y to each child upon attainment of age 21. They will establish the trust fund with a single investment of Z. Find the equation of value for Z. ?

Answer 1

Answer:

The equation of Z is: $Z=X(v^{17}+v^{15}+v^{12})+Y(v^{20}+v^{18}+v^{15})$

Step-by-step explanation:

• The first child is of age 1 year.

        Then the amount invested for the 1-year old is: $Xv^{17}+Yv^{20}$

• The second child is of age 3 years.

        Then the amount invested for the 3-year old is: $Xv^{15}+Yv^{18}$

• The third child is of age 6 years.

        Then the amount invested for the 6-year old is: $Xv^{12}+Yv^{15}$

The one-time investment will be:

$Z=Xv^{17}+Yv^{20}+Xv^{15}+Yv^{18}+Xv^{12}+Yv^{15}\\=X(v^{17}+v^{15}+v^{12})+Y(v^{20}+v^{18}+v^{15})$