Jackson's salary can be decomposed into three components $($all after income tax$)$:

An annual base salary of $$60,000$ and it will increase by $6\%$ every year at the beginning of each year.

A sign$-$on bonus of $$20,000,$ paid with his first salary.

Performance bonus paid at the end of each year. His bonus in year t$,$ B$($t$)$ is calculated using the following formula:

B$($t$)=0\mathrm{.}15$A$($t$)*$ I$($t$)*$exp$(1/$t$),$

where A$($t$)$ is his base salary for year t$,$ and I$($t$)$ is a Bernoulli random variable with success probability p $=0\mathrm{.}8.$ Calculate exactly the probability that Jackson's total performance bonus $($nominal amount$)$ will be no less than $$90,000.$