1. Identify the Variables

- Principal ( $P$ ):$ 38,700
- Annual Interest Rate $(r): 6.2 %=0.062$

- Compounding frequency ( $n$ ): 12 (monthly)

- Monthly Interest Rate $\((i): r / n=0.062 / 12 \approx 0.0051667\)$

- Total Time: 3 years $=36$ months.

2. Find the Balance at the Start of the Last Month

The interest for the 36th month is calculated based on the balance accumulated by the end of the 35th month. We use the compound interest formula:

$$
\(A=P\left(1+\frac{r}{n}\right)^{n t}\)
$$


For 35 months:

$$
\(\begin{gathered}
A_{35}=38,700 \times\left(1+\frac{0.062}{12}\right)^{35} \\
A_{35} \approx 38,700 \times(1.0051667)^{35} \\
A_{35} \approx 38,700 \times 1.19765 \approx \$ 46,349.36
\end{gathered}\)
$$

3. Calculate Interest for Month 36

Now, we apply the monthly interest rate to this balance:

$$
\(\begin{gathered}
\text { Interest }_{36}=\text { Balance }_{35} \times i \\
\text { Interest }_{36}=46,349.36 \times\left(\frac{0.062}{12}\right) \\
\text { Interest }_{36} \approx 46,349.36 \times 0.0051667 \approx \$ 239.47
\end{gathered}\)
$$