Question

​Boden's account has a principal of ​$500 and a simple interest rate of 3.3​%. 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?
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Question content area bottom
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 how much money will be in Boden's account after 4 years, we first need to determine the simple interest earned over that time. The formula for calculating simple interest is:

\[
\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}
\]

Given:
- Principal = $500
- Rate = 3.3% = 0.033 (as a decimal)
- Time = 4 years

Now, we can plug in the values into the formula:

\[
\text{Interest} = 500 \times 0.033 \times 4
\]

Calculating that step by step:

1. Calculate \(0.033 \times 4\):
\[
0.033 \times 4 = 0.132
\]

2. Now multiply by the principal:
\[
\text{Interest} = 500 \times 0.132 = 66
\]

So, the interest earned over 4 years is $66.

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

\[
\text{Total Amount} = \text{Principal} + \text{Interest}
\]
\[
\text{Total Amount} = 500 + 66 = 566
\]

Now, to answer your questions regarding the double number line:

1. The missing interest value for 4 years, based on the calculations above, is **$66**.
2. The corresponding year value is **4 years**.

Thus, you can fill in the blanks as follows:

- Missing interest value: **66** (for 4 years)
- Missing year value: **4** (for the interest amount of 66)

Let me know if you need any further assistance!