Question

If you invest $5,000 dollars in an account that will earn 6.5% compounded continuously, how much will it be worth after 8 years? (A=Pe^rt)

Answer 1

Given the Amount function in the question as written below

$A=Pe^{rt}$$\begin{gathered} A=\text{Amount} \\ P=Principal,amount\text{ invested} \\ r=\text{rate} \\ t=\text{time} \end{gathered}$

Write out the parameters given in the question

$P=\text{ \ 5,000; r=6.5\%; t=8years; e= natural number, constant=2.718}$

Substitute for the parameters in the Amount function given

$\begin{gathered} r=\frac{6.5}{100}=0.065 \\ A=5000e^{0.065\times8} \end{gathered}$$\begin{gathered} A=5000e^{0.52} \\ A=5000(1.6820276497) \\ A=8410.1382 \end{gathered}$

Hence, the worth of the investment would be $8410.14