The accumulated, or total, future value after $T$ years of an income stream of $R(t)$ thousand dollars per year, earning interest at the rate of $r$ per year compounded continuously, is given by

$A=e^{rT}{\displaystyle \underset{0}{\overset{T}{}}}R(t)e^{-rt}dt$

A company recently bought an automatic car$-$washing machine that is expected to generate $4$ thousand dollars in revenue per year, $t$ years from now, for the next $10$ years. If the income is reinvested in a business earning interest at the rate of $r=10\%$ per year compounded continuously, find the total accumulated value of this income stream at the end of $10$ years.

Answer: $A=$

$($thousand dollars$).$