Use the model $A=P e^{r t}$ or $A=P\left(1+\frac{r}{n}\right)^{n t}$, where $A$ is the future value of $P$ dollars invested at interest rate $r$ compounded continuously or $n$ times per year for $t$ years. Victor puts aside $\$ 8000$ in an account with interest compounded continuously at $2.5 \%$. How long will it take for him to earn $\$ 2000$ ? Round to the nearest month. It will take approximately years and months for him to earn $\$ 2000$.

Step 1 ：We are given the principal amount (P) as $8000, the rate of interest (r) as 2.5% or 0.025 (in decimal form), and the future amount (A) as $8000 + $2000 = $10000. We need to find the time (t) it will take for the principal to grow to the future amount. We can use the formula for continuous compounding to solve for t.

Step 2 ：The formula for continuous compounding is \(A=P e^{r t}\). We can rearrange this formula to solve for t: \(t = \frac{1}{r} \ln(\frac{A}{P})\).

Step 3 ：Substitute the given values into the formula: P = 8000, r = 0.025, A = 10000.

Step 4 ：Solving the equation gives t = 8.92574205256839.

Step 5 ：Converting the decimal part of the year to months, we get approximately 11 months.

Step 6 ：Final Answer: It will take approximately \(\boxed{8}\) years and \(\boxed{11}\) months for him to earn $2000.