Answer
$47416.72$ dollars
Work Step by Step
The flow of rate of the investment stream can be expressed as: $R(t)=8000 $ dollars per year.
We have: $r=0.042$ and $T=15 \ years$
The future value is equal to: $\int_0^{15} 8.000 e^{0.042 (15-t)} \ dt =167163.92 $ dollars
Therefore, the present value is equal to:$\dfrac{\ Future Value}{e^{rT}}=\dfrac{167163.92 }{e^{0.042 (15-t)}}=89030.13$ dollars
Now, the initial value is equal to:
$\dfrac{89030.13}{e^{0.042 \times 15}}=47416.72$ dollars