You are given the following.

$($i$.)$ A $2n$ year annuity immediate pays $300$ for the first $n$ years and $500$ for the second $n$ years. When the annual effective interest rate is $i,$ the present value for the annuity is $2249\mathrm{.}087675.$

$($ii$.)$ An $n$ year deferred $n$ year annuity immediate paying $600$ per year has a present value of $1495\mathrm{.}845665.$ This is also based on an annual effective interest rate of $i.$

$($iii$.)$ A $3n$ year annuity immediate pays $700$ per year. If the present value is $i$ in the odd numbered years and $i-0\mathrm{.}01$ in the even numbered years, the present value is $P.$

Calculate $P.$