To determine the amount of simple interest Nina will earn after 3 months with an annual interest rate of 2.2%, we need to follow a step-by-step process.
1. Identify the principal amount, the annual interest rate, and the time period:
- Principal (P) = [tex]$3400
- Annual Interest Rate (r) = 2.2% = 0.022 (as a decimal)
- Time Period (t) = 3 months
2. Convert the time period from months to years:
Since the interest rate is per year, we need to express the time period in years. There are 12 months in a year, so:
\[
\text{Time in years} = \frac{3 \text{ months}}{12 \text{ months per year}} = 0.25 \text{ years}
\]
3. Use the simple interest formula:
Simple interest (I) is calculated using the formula:
\[
I = P \times r \times t
\]
Substituting the given values:
\[
I = 3400 \times 0.022 \times 0.25
\]
4. Calculate the interest:
\[
I = 3400 \times 0.022 \times 0.25 = 3400 \times 0.0055 = 18.70
\]
Therefore, the interest Nina will earn after 3 months is \(\$[/tex]18.70\).
Thus, the correct answer from the options given is:
[tex]\[
\$ 18.70
\][/tex]
