Robert is saving for his son's education and will need to do so in stages as he started late on this important goal and was not sure if his son would attend university. He is looking to invest $$15,000$ at $5\%,$ compounded semi$-$annually, for $3$ years. He will then take the total proceeds at maturity, add $$1,100,$ and reinvest it at $4\%,$ compounded monthly, for an additional $2$ years. How much money will he have in $5$ years' time?

Select one:

O a$.$ $$20,004$

O b$.$ $$18,587$

O c$.$ $$20,033$

O d$.$ $$19,815$