ulie has just retired. Her company$$s retirement program has two options as to how retirement benefits can be received. Under the first option, Julie would receive a lump sum of $$135,000$ immediately as her full retirement benefit. Under the second option, she would receive $$18,000$ each year for $12$ years plus a lump$-$sum payment of $$54,000$ at the end of the $12-$year period.

Required:

$1-$a$.$ Calculate the present value for the following assuming that the money can be invested at $11\%.$

$1-$b$.$ If she can invest money at $11\%,$ which option would you recommend that she accept?