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This is a compound interest problem. To find how much money will be in the account after 3 years, we can use the compound interest formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $A$ is the amount of money in the account after time $t$,
- $P$ is the principal amount (initial deposit),
- $r$ is the annual interest rate (in decimal form),
- $n$ is the number of times the interest is compounded per year,
- $t$ is the time the money is invested or borrowed for, in years.

From the problem:
- $P = 5000$,
- $r = 0.2\%$ per year $= 0.002$,
- $n = 4$ (since the interest is compounded quarterly),
- $t = 3$ years.

Now, substituting these values into the formula:

\[
A = 5000 \left(1 + \frac{0.002}{4}\right)^{4 \times 3}
\]

Let's compute the result:

\[
A = 5000 \left(1 + 0.0005\right)^{12}
\]
\[
A = 5000 \times (1.0005)^{12}
\]
\[
A = 5000 \times 1.006006
\]
\[
A \approx 5030.03
\]

The amount of money in the account after 3 years is approximately **$5030.03**.

Would you like more details or have any questions? 

Here are some related questions you might find helpful:
1. How does changing the interest rate affect the final amount?
2. What if the compounding was monthly instead of quarterly?
3. How much interest was earned after 3 years?
4. What happens if the initial deposit was higher, say $10,000?
5. How would the formula change for continuous compounding?

**Tip:** Always remember to convert percentage rates to decimals before plugging them into formulas.

Find how much money will be in the account after 3 years, with a principal of $5,000, an interest rate of 0.2% compounded quarterly.

Learn how to calculate compound interest on a principal of $5000 at an annual interest rate of 0.2%, compounded quarterly, over 3 years. This example explains the use of the compound interest formula with step-by-step solutions.

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