To find the missing quantity using the simple interest formula:

$I = P \cdot r \cdot t$

where:

• $I$ is the interest,
• $P$ is the principal (initial amount),
• $r$ is the interest rate (as a decimal),
• $t$ is the time in years.

In your case, you are given:

• $P = 500$ (the principal),
• $r = 13\% = 0.13$ (the interest rate in decimal form),
• $t = 2$ years (the time).

Now, we can calculate the interest $I$ using the formula:

$I = 500 \cdot 0.13 \cdot 2$

Let me compute this for you.The interest $I$ is calculated to be $130.

Summary:

• Principal (P): $500
• Rate (r): 13% (or 0.13 as a decimal)
• Time (t): 2 years
• Interest (I): $130

Would you like more details or further clarification?

Here are 5 related questions to explore:

1. How would the interest change if the rate was 10% instead of 13%?
2. What would the total amount be after 2 years (Principal + Interest)?
3. How would the interest change if the time was 3 years instead of 2?
4. What would happen to the interest if you doubled the principal to $1000?
5. How can you rearrange the formula to solve for $r$ (rate) if the interest and time are known?

Tip: Always convert percentages to decimal form (e.g., 13% becomes 0.13) when using the simple interest formula!