# Finance - Present Value of Perpetuity

I'm having trouble solving this perpetuity problem

Assume this is the case for a hypothetical company that is expected to pay half-yearly dividends of $0.20$ forever, with the first dividend payable in six months’ time. If you purchased the stock two months before the next dividend of $0.20$ is due, and the company is expected to maintain this dividend forever, what is the price you would pay if you expect a return on equity of $16\%$ p.a.?

So far I have:

Price pay = (Dividend/interest rate) $*(1+i)^n$

Price pay = $(0.2/0.08)*(1+0.08)^{4/6}$

But the book says

Price pay = $(0.2/0.08)*(1+0.08)^{2/6}$

I don't understand why they use $2$ instead of $4$

Thanks !

Presumably if you had bought the perpetuity immediately after a dividend payment, you would have expected to pay $\frac{0.20}{0.16/2}=\frac{0.20}{0.08}$
If you had bought the perpetuity immediately before a dividend payment, you would have scaled this up by a factor of $1+0.08$
But in fact you purchased the stock $2$ months before the next dividend is due rather than $6$ months before, so your scaling factor would be by $(1+0.08)^{(6-2)/6} = (1+0.08)^{4/6}$ as you have