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

Which of the following is the correct equation of value for Z?

• [[math]]\frac{X}{v^{17}+v^{15}+v^{12}}+\frac{Y}{v^{20}+v^{18}+v^{15}}[[/math]]
• [[math]]3\left(X v^{18}+Y v^{21}\right)[[/math]]
• [[math]]3 X v^3+Y\left(v^{20}+v^{18}+v^{15}\right)[[/math]]
• [[math]](X+Y) \frac{v^{20}+v^{18}+v^{15}}{v^3}[[/math]]
• [[math]]X\left[v^{17}+v^{15}+v^{12}\right]+Y\left[v^{20}+v^{18}+v^{15}\right][[/math]]

References

Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.

Solution: C

Child 1 needs [math]X v^3+Y v^{21-1}[/math].

Child 2 needs [math]X v^3+Y v^{21-3}[/math].

Child 3 needs [math]X v^3+Y v^{21-6}[/math]

So total amount needed is [math]3 X v^3+Y\left(v^{20}+v^{18}+v^{15}\right)[/math].

References

Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.