The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume

365
 
days in a year.

Pequals

​$15 comma 000

​,

requals

8

​%,

tequals

150
 
days

The formula for simple interest is:

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

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

### Step-by-step:

1. Convert $ r = 8\% $ to a decimal by dividing by 100:
   \[
   r = \frac{8}{100} = 0.08
   \]

2. Convert the time $ t = 150 $ days into years. Since there are 365 days in a year:
   \[
   t = \frac{150}{365} \approx 0.41096 \text{ years}
   \]

3. Now, apply the simple interest formula:
   \[
   I = 15000 \times 0.08 \times 0.41096
   \]

Let me calculate the result for you.The simple interest owed for the use of the money is approximately **$493.15**.

Would you like further clarification or additional details? 

Here are 5 related questions for further exploration:
1. How would the interest change if the time period were 200 days instead of 150?
2. What would the interest be if the principal was $20,000 at the same rate and time?
3. How does simple interest differ from compound interest?
4. How much total money (principal + interest) would need to be repaid after 150 days?
5. What is the impact of using a 360-day year convention on this calculation?

**Tip:** Always express interest rates as decimals when performing calculations to avoid errors.

The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume 365 days in a year. P = $15,000, r = 8%, t = 150 days.

Learn how to calculate the simple interest owed on a principal of $15,000 at an 8% interest rate over a period of 150 days. This solution uses the simple interest formula, covers time conversion from days to years, and provides a detailed calculation. Suitable for students in Grades 9-10.

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