Nathan is shopping for an $2$n$-$year long investment that pays interest compounded annually

and doubles in n years, that is$,$ a$($n$)=2$ where a$($t$)=(1+$ i$)^$t$.$ Nathan wishes to accumulate $$100,000$

at the end of $2$n years by making a $$2,000$ deposit at the end of each of the first n years, and a $$3,000$

deposit at the end of each of the next n years. Find the desired effective rate of interest i$.$