Given an interest rate of $10$ percent per year, what is the value at date $t=5$ of a perpetual stream of $$500$ payments with the first payment at date $t=12?$

Multiple Choice

$$2,565\mathrm{.}79$

$$5,100\mathrm{.}00$

$$2,822\mathrm{.}37$

$$2,878\mathrm{.}82$

$$2,765\mathrm{.}92$