$7\mathrm{.}1\mathrm{.}5$ Develop an expression for the duration of a level $n-$payment

annuity$-$immediate of $1$ per period with interest rate i per period,

and show that it is equal to $\frac{1}{d}-\frac{n}{i{s}_{\frac{?}{\text{b}\text{a}\text{r}}(ni)}}.$