Question $2(2\mathrm{.}5$ points$)$

An annuity pays $1$ at the end of each

year for $n$ years. Using an annual

effective interest rate of $i,$ the

accumulated value of the annuity at

time $(n+1)$ is $30\mathrm{.}772.$ It is also known

that $(1+i{)}^n=3\mathrm{.}797.$

Calculate n$.$

$14$

$17$

$13$

$12$

$11$