​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?

Question

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.