Jackson plans to make $10$ annual deposits of $$1,000$ starting $5$ years from today. At a rate of $4\%,$ compounded semi$-$annually, how much will he have $20$ years from today? Round your final answer to the nearest dollar.

a$)$ $$12,514$

b$)$ $$15,255$

c$)$ $$15,871$

d$)$ $$16,021$