A continuous annuity with withdrawal rate $N=$$$800/$year and interest rate $r=5\%$ is funded by an initial deposit $P_0.$

$($a$)$ When will the annuity run out of funds if $P_0=$$$13,000?$

The annuity runs out after approximately years.

Answer to the nearest whole year.

$($b$)$ Which initial deposit $P_0$ yields a constant balance? $P_0=$$