The formula for compounded continuously is :
[tex]A=Pe^{rt}[/tex]where A is the future amount
P is the initital amount
e is some constant approximately equal to 2.71828...
r is the rate of interest and
t is the time in years
From the given problem,
P = 8500
r = 6.75% or 0.0675
t = 25 years
Using the formula above, the value of A after 25 years is :
[tex]\begin{gathered} A=8500e^{0.0675(25)} \\ A=45950.57 \end{gathered}[/tex]The answer is $45,950.57
