Matemática financeira

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Boa tarde!

n=5
PMT=30000
i=12%a.a.
k=2 anos (diferida)

[latex]PV=PMT\cdot\left[\frac{1-\left(1+i\right)^{-(n+k)}}{i}-\frac{1-\left(1+i\right)^{-k}}{i}\right]\\
PV=30\,000\cdot\left[\frac{1-\left(1+12\%\right)^{-(5+2)}}{12\%}-\frac{1-\left(1+12\%\right)^{-2}}{12\%}\right]\\
PV=30\,000\cdot\left(\frac{1-1,12^{-7}}{0,12}-\frac{1-1,12^{-2}}{0,12}\right)\\
PV\approx 86\,211,17
[latex]

Para valor futuro:
[latex]FV=PV\cdot(1+i)^{n+k}\\
FV\approx 86\,211,17\cdot(1+12\%)^{5+2}\\
FV\approx 86\,211,17\cdot 1,12^{7}\\
FV\approx 190\,585,42[latex]

Espero ter ajudado!