Problem $3$ At an annual effective interest rate $\backslash ($ i $\backslash )$ it is known that: $($i$)$ The present value of $3$ at the end of each year for $\backslash (3$ n $\backslash )$ years, plus an additional $1$ at the end of each of the first $\backslash (2$ n $\backslash )$ years, is $7.($ii$)$ The present value of an $\backslash (2$ n $\backslash )-$year deferred annuity$-$immediate paying $1$ per year for $\backslash ($ n $\backslash )$ years is $1.$ Find $\backslash ($ i $\backslash ).$