Question

​Boden's account has a principal of ​$700 and a simple interest rate of 3.9​%. Complete the number line. How much money will be in the account after 4​ years, assuming Boden does not add or take out any​ money?
font size increased by 8 interestfont size increased by 8 yearsfont size increased by 2 27.30font size increased by 2 54.60font size increased by 2 81.90font size increased by 2 0font size increased by 2 1font size increased by 2 2font size increased by 2 3



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Part 1
In the double number​ line, the missing interest value is
  
enter your response here and the missing year value is
  
enter your response here.
​(Type integers or​ decimals.)

Answer 1

To calculate the amount of simple interest earned and the total amount in Boden's account after 4 years, we can use the formula for simple interest:

\[
I = P \times r \times t
\]

Where:
- \(I\) is the interest,
- \(P\) is the principal amount ($700),
- \(r\) is the rate of interest (3.9%, or 0.039 as a decimal),
- \(t\) is the time in years (4 years).

First, we calculate the interest:

\[
I = 700 \times 0.039 \times 4
\]
\[
I = 700 \times 0.156
\]
\[
I = 109.2
\]

Now we add the interest earned to the principal to find the total amount in the account after 4 years:

\[
\text{Total amount} = P + I = 700 + 109.2 = 809.2
\]

### Now, filling in the missing values for the double number line:

To fill out the double number line, we need to find the interest value and year value corresponding to each year from 0 to 4.

From the interest of 109.2 after 4 years, we can infer the linear growth of interest per year:

1. **After 0 years**: Interest = $0 (Year = 0)
2. **After 1 year**:
\[
I_1 = 700 \times 0.039 \times 1 = 27.30 \quad \text{(Approx.)}
\]
3. **After 2 years**:
\[
I_2 = 700 \times 0.039 \times 2 = 54.60 \quad \text{(Approx.)}
\]
4. **After 3 years**:
\[
I_3 = 700 \times 0.039 \times 3 = 81.90 \quad \text{(Approx.)}
\]
5. **After 4 years**:
\[
I_4 = 700 \times 0.039 \times 4 = 109.20
\]

So, on the number line:
- The missing interest value after 4 years is **109.20**.
- The missing year value for this interest is **4**.

### Final Answers:
- The missing interest value is **109.20**.
- The missing year value is **4**.