Given:
[tex]\begin{gathered} rate(r)=6\% \\ time=10years \\ Amount(Balance-after-10years)=32450 \end{gathered}[/tex]To Determine: The initial investment
Solution
The initial investment is the principal. This can calculated using the compounded continuously formula
[tex]\begin{gathered} A=Pe^{rt} \\ A=Amount \\ P=Principal \\ r=rate \\ t=time \end{gathered}[/tex]Substitute the given into the formula
[tex]\begin{gathered} 32450=Pe^{0.06\times10} \\ 32450=Pe^{0.6} \end{gathered}[/tex][tex]\begin{gathered} P=\frac{32450}{e^{0.6}} \\ P=\frac{32450}{1.8221188} \\ P=17808.94 \end{gathered}[/tex]Hence, the initial investment is $17,808.94
