George, aged $50,$ is considering purchasing two annuities:

$($i$)$ a $20-$year annuity certain with an annual benefit of $$10,000$ payable continuously, or

$($ii$)$ a $20-$year temporary life annuity with an annual benefit of $$10,000$ payable continuously.

The cost for either annuity is its single benefit premium.

George opts for the temporary life annuity, and he invests the savings $($the difference in single benefit premiums$)$ immediately. George survives the $20$ years. You may assume that $=0\mathrm{.}04$ and $=0\mathrm{.}06.$

Determine the value of the invested savings after the $20$ years.

$($A$)$ Less than $$80,000$

$($B$)$ At least $$80,000,$ but less than $$105,000$

$($C$)$ At least $$105,000,$ but less than $$130,000$

$($D$)$ At least $$130,000,$ but less than $$155,000$

$($E$)$ At least $$155,000$