Answer
(a) 2145.02 dollars
(b) 2300.55 dollars
(c) 3043.92 dollars
Work Step by Step
The formula to calculate the value of an investment that is compounded continuously at a given rate is P(t)=Pe^((r)(t))
Where P(t)= the value of an investment at t, P=principal amount, r= rate, and t= time
From the question we know that p=2000 and r= .035 giving us the formula
P(t)=2000e^((.035)(t))
What is the value of the investment after
(a) 2 years
P(2)=2000e^((.035)(2))
p(2)= 2145.02 dollars
(b) 4 years
P(4)=2000e^((.035)(4))
p(4)= 2300.55 dollars
(c) 12 years
P(12)=2000e^((.035)(12))
P(12)= 3043.92 dollars