Problem $3$ At an annual effective interest rate i it is known that:

$($i$)$ The present value of $3$ at the end of each year for $3$n years, plus an additional $1$ at the end of each of

the first $2$n years, is $7.$

$($ii$)$ The present value of an $2$n$-$year deferred annuity$-$immediate paying $1$ per year for n years is $1.$

Find i$.$