Respuesta :
Solution:
The continuous compound interest formula is expressed as
[tex]\begin{gathered} A=P\times e^{rt} \\ where \\ A\Rightarrow final\text{ amount} \\ P\Rightarrow initial\text{ investment} \\ e\Rightarrow Napier^{\prime}sNumber≅2.7183 \\ r\Rightarrow interest\text{ rate} \\ t\Rightarrow time \end{gathered}[/tex]Given that $10 is invested at 10% compounded continuously after a period of 3 years, this implies that
[tex]\begin{gathered} P=10 \\ r=10\%\text{=0.1} \\ t=3\text{ } \end{gathered}[/tex]The amount that results from the investment is evaluated by substituting these above values into the equation.
Thus,
[tex]\begin{gathered} A=10\times(\text{2.7183\rparen}^{(0.1\times\text{3\rparen}} \\ =10\times(2.7183)^{0.3} \\ =10\times\text{1.349861515} \\ =13.49861515 \\ \Rightarrow A\approx\$\text{13.5 \lparen nearest cent\rparen} \end{gathered}[/tex]Hence, the amount that results from the investment is evaluated to be $13.5 (nearest cent).
