Find the present value of a perpetuity with payments every two years beginning immediately where the payments have the form p, p + q, p + 2q, p + 3q, . . .

References

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

[[math]] \begin{aligned} P V & =p+(p+1 q) v^2+(p+2 q) v^4+(p+3 q) v^6+\cdots=p\left(1+v^2+v^4+\ldots\right)+q v^2\left(1+2 v^2+3 v^4+\ldots\right) \\ & =\frac{p}{1-v^2}+q v^2\left(1+v^2+v^4+\ldots\right)\left(1+v^2+v^4+\ldots\right)=\frac{p}{1-v^2}+\frac{q v^2}{\left(1-v^2\right)^2}\end{aligned} [[/math]]

References

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