a perpetuity pays 1 every january 1 starting in 2020. The effective rate of interest will be i in odd numbered years and j in even-numbered years. Find an expression for the present value of the perpetuity on January 1, 2019.

The correct solution is Vj[1+Vi]*[1/(1-VjVi)] but i do not understand how this works. I know the formula to find the present value of a perpetuity is D/r, so i thought it would be .5[1/i+i/j] since each of the formulas for i and j are only half of the years. Please fix my logic here.

Contrary to the comment below there are no factors missing to solve this problem, granted you know the material. I provided the solution, which i found was based on a formula made specifically for even and odd year problems. I simply need someone who understands the material to give a step by step to get the solution with explanation if possible. Thanks in advance, it would be very helpful.