Question

How much time must you invest $8500 at 6.25% compounded continuously tohave $13840.04? Round the time t to 2 decimal places.

Answer 1

Write out the compound interest formula

$A=Pe^{rt}$

Where A= The final Amount after the compound interest

P= The initial amount invested

r=rate

t=time

Write out the given parameters in the question

$\begin{gathered} P=\text{ \ 8500} \\ r=6.5\text{ \%} \\ t=\text{unknown} \\ A=\text{ \ 13840.04} \\ e=2.71828 \end{gathered}$$\begin{gathered} 13840.04=8500\times e^{0.0625t}^{} \\ e^{0.0625t}=\frac{13840.04}{8500} \\ e^{0.0625t}=1.62824 \end{gathered}$$\begin{gathered} 0.0625t=In(1.62824) \\ 0.0625t=0.4875997 \end{gathered}$$\begin{gathered} t=\frac{0.4875997}{0.0625} \\ t=7.79999483 \end{gathered}$$t=7.80(\text{nearest 2 decimal places)}$

Hence, the time required for the compounded continuous investment is 7.80