Question

g 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

Z=X(v¹⁷+v¹⁵+v¹²) + Y(v²⁰+v¹⁸+v¹⁵)

Explanation:

For the the first child of age 1 yea to be paid an investment of X at age 18 will be Xv¹⁷ and an investment of Y at age 21 will be Yv²⁰·

also for then 3 years old child to be paid an investment of X at age 18 will be Xv¹⁵ and an investment of Y at age 21 will be Yv¹⁸

lastly for the 6 years old child be paid an investment of X at age 18 will be Xv¹² and an investment of Y at age 21 will be Yv¹⁵·

Hence the investment Z must be equal to the summation of all this values

Z=X(v¹⁷+v¹⁵+v¹²) + Y(v²⁰+v¹⁸+v¹⁵)