Answer:
[tex]V(t)=2000(1.02)^t[/tex]
Step-by-step explanation:
To solve the problem, we use the compound interest formula.
The formula that gives the total value V(t) of the investment after t years is:
[tex]V(t) = V_0(1+r)^t[/tex]
where
[tex]V_0[/tex] is the initial value of the investment
r is the interest rate
t is the time (in years)
V(t) is the value of the investment after t years
In this problem:
[tex]V_0=\$2000[/tex] is the initial investment
[tex]r=2\% = 0.02[/tex] is the interest rate
Substituting, we find the final expression for this problem:
[tex]V(t)=2000(1+0.02)^t[/tex]
which can be reduced to
[tex]V(t)=2000(1.02)^t[/tex]
