Answer:
a) The present value is 688.64 $
b) The accumulated amount is 1532.60 $
Step-by-step explanation:
a) The preset value equation is given by this formula:
[tex]P=\int^{T}_{0}f(t)e^{-rt}dt[/tex]
where:
So we have:
[tex]P=\int^{T}_{0}(0.01t+100)e^{-rt}dt[/tex]
Now we just need to solve this integral.
[tex]P=\int^{T}_{0}0.01te^{-rt}dt+\int^{T}_{0}100e^{-rt}dt[/tex]
[tex]P=e^{-0.08t}(-1.56-0.13t)|^{10}_{0}+1250e^{-0.08t}|^{10}_{0}[/tex]
[tex]P=0.30+688.34=688.64 $[/tex]
The present value is 688.64 $
b) The accumulated amount of money flow formula is:
[tex]A=e^{r\tau}\int^{T}_{0}f(t)e^{-rt}dt[/tex]
We have the same equation but whit a term that depends of τ, in our case it is 10.
So we have:
[tex]A=e^{r\tau}\int^{T}_{0}(0.01t+100)e^{-rt}dt=e^{0.08\cdot 10}P[/tex]
[tex]A=e^{0.08\cdot 10}688.64=1532.60 $[/tex]
The accumulated amount is 1532.60 $
Have a nice day!
