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=(6.5)/(100)=0.065 \\ A=5000e^(0.065*8) \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