Answer:
$3,040.00
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]
Given:
- A =$8,441.60
- r = 6% = 0.06
- t = 17 years
Substitute the given values into the continuous compounding formula and solve for P:
[tex]\implies 8441.60=Pe^{0.06 \times 17}[/tex]
[tex]\implies 8441.60=Pe^{1.02}[/tex]
[tex]\implies P=\dfrac{8441.60}{e^{1.02}}[/tex]
[tex]\implies P=3043.99824...[/tex]
Therefore, the amount of the initial investment is $3,040.00 (rounded to the nearest tens place).
