If it were an annual reinvestment, what would be the rate it is reinvested in? Would this require the question to give as a yield curve to do the pricing?
Ignoring the initial cash flow is important in order to compute the duration since it takes all the future cash flows.
The problem, as you point it out, is that we don't know if it's a monthly or an annual reinvestment. But since it's a question following that of the ytm, I bet this is an annual reinvestment.