Billy deposits $$800$ at the end of every $3-$months in a fund earning interest at j$4=12\%.$ At the end of $3$ years, the interest rate changes to j$4=8\%.$ What is the accumulated value immediately after his $20$th deposit?

a

$$18,220\mathrm{.}00$

b

$$20,168\mathrm{.}95$

c

$$21,248\mathrm{.}81$

d

$$21,496\mathrm{.}30$