Respuesta :
We will investigate the continuous compounding evaluation of an initial investment.
The formulation used for continuous compounding to express the future value ( A ) is represented by:
[tex]A\text{ = P}\cdot e^{r\cdot t}[/tex]Where,
[tex]\begin{gathered} P\colon\text{ Present Value} \\ r\colon\text{ Rate ( Annual )} \\ t\colon time\text{ in years} \end{gathered}[/tex]The following investment ( P ) was made at an anual interest ( r ). We are to determine the amount in the bank account after ( t ) years from now:
[tex]P\text{ = \$500 , r = 4.1\% , t = 10 years }[/tex]The amount accumulated in the bank account can be determined from the given formulation as follows:
[tex]\begin{gathered} A\text{ = 500}\cdot e^{\frac{4.1}{100}\cdot10} \\ A\text{ = 500}\cdot e^{0.41} \\ A\text{ = }753.40889 \end{gathered}[/tex]The solution rounded to the nearest dollar is:
[tex]\text{\$}753[/tex]
