Answer:
It would be $ 635.62.
Step-by-step explanation:
Since, when an amount is increasing compound continuously,
Then the amount after t years,
[tex]A=Pe^{rt}[/tex]
Where P is the principal amount,
r is the annual rate,
Here, P = $ 500,
r = 6 % = 0.06,
t = 4 years,
Thus, the amount after 4 years,
[tex]A=500 e^{0.06\times 4}[/tex]
[tex]=500 e^{0.24}[/tex]
[tex]=\$ 635.624575161\approx \$ 635.62[/tex]
Hence, $500 would be $ 635.62 after 4 years with the rate of 6% compounded continuously.
