The present value of an annuity$-$certain of $1$ p$.$a$.$ payable for an exact number of years at a given effective rate of interest is $23\mathrm{.}19594,$ if payments are made half$-$yearly; and $23\mathrm{.}31032$ if payments are made quarterly.

The amount of the annuity if payments were made yearly would be $282\mathrm{.}6619.$

Calculate the term of the annuity and the effective rate of interest p$.$a$.$