We are given
initial amount is $2000
so, [tex] P=2000 [/tex]
annual interest rate is 5.1%
so, [tex] r=0.051 [/tex]
time is 3 years
so, [tex] t=3 [/tex]
it is compounded continuously
so, we can use amount formula
[tex] A=Pe^{rt} [/tex]
where A is amount after t years
P is initial amount
r is interest rate
t is time in years
now, we can plug values
[tex] A=2000e^{0.051*3} [/tex]
we get
[tex] A=2330.6499 [/tex]
[tex] A=2330.65 [/tex]
So, Amount after 3 years is $2330.65.........Answer
