A life insurance policy issued to a life aged $50$ pays $$2000$ at the end of the quarter year of death before age $65$ and $$1000$ at the end of the quarter year of death after age $65.$ Use the Standard Ultimate Life Table and assuming interest at $5\%$ per year, in the following.

$($a$)$ Calculate the EPV of the benefit.

$($b$)$ Calculate the standard deviation of the present value of the benefit.