Continuous Compound
An initial investment of P dollars at an interest annual rate r will have a final value A given by:
[tex]A=P\cdot e^{r\cdot t}[/tex]
The investment is P = $15,000 at a rate of r = 4.5% = 0.045. The accumulated (or final) value for t = 5 years is:
[tex]\begin{gathered} A=15,000\cdot e^{0.045\cdot5} \\ \text{Calculating:} \\ A=15,000\cdot e^{0.225} \\ A=15,000\cdot1.252323 \\ A=18,784.84 \end{gathered}[/tex]
The Accumulated value is $18,784.84
