Find the rate. Round to the nearest tenth of a percent.

Principal: $1,075
Time: 18 days
Interest: $4.62
Select one:

A.
4.3%

B.
7.7%

C.
8.7%

D.
8.6%

To find the interest rate, we can use the simple interest formula:

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

where:
- $ I $ is the interest,
- $ P $ is the principal,
- $ r $ is the rate (expressed as a decimal),
- $ t $ is the time (in years).

Given:
- Principal ($ P $) = $1,075
- Time ($ t $) = 18 days (converted to years: $ \frac{18}{360} $)
- Interest ($ I $) = $4.62

First, convert the time from days to years:

\[ t = \frac{18}{360} = 0.05 \text{ years} \]

Now, rearrange the simple interest formula to solve for $ r $:

\[ r = \frac{I}{P \times t} \]

Plugging in the given values:

\[ r = \frac{4.62}{1075 \times 0.05} \]

\[ r = \frac{4.62}{53.75} \]

\[ r \approx 0.0859 \]

To express this as a percentage, multiply by 100:

\[ r \approx 0.0859 \times 100 = 8.59\% \]

Rounding to the nearest tenth of a percent:

\[ r \approx 8.6\% \]

So the correct answer is:

**D. 8.6%**

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Do you want details or have any questions? Here are 8 related questions for further exploration:

1. How would the interest rate change if the interest was $5.00 instead of $4.62?
2. What would be the interest if the principal was $1,500 with the same rate and time period?
3. How does the length of the time period affect the interest rate calculation?
4. What is the formula to convert days into years for interest calculations?
5. How would the principal amount change the required rate to achieve a specific interest amount?
6. How does rounding to the nearest tenth of a percent affect the accuracy of financial calculations?
7. What would the rate be if the time period was 30 days instead of 18 days?
8. Can you explain the difference between simple interest and compound interest?

**Tip:** Always ensure to convert time periods into consistent units (like years) when calculating interest rates.

Learn how to find the interest rate using the simple interest formula. Solve the problem involving a principal of $1,075, time period of 18 days converted to years, and an interest of $4.62. Round the rate to the nearest tenth of a percent. Suitable for high school students learning about simple interest and percentage calculations.

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