You have two perpetuities, with the same yearly cash flows and the same risk $($i$.$e$.,$ the same discount rate$).$ However, the first perpetuity has its payments starting at Year $1,$ while the second perpetuity has its payments starting at year $21.$ Also, the first perpetuity has a value of $$1,500$ when evaluated as of Year $0.$

Now, consider a $20-$year annuity $($payments in Years $1-20),$ created as the difference between perpetuities $1$ and $2.$ It has a value of $$1,206\mathrm{.}58$ when evaluated as of Year $0$ and using the same discount rate as applied to the perpetuities.

Determine the discount rate that is being used to evaluate the perpetuitie