To find the simple interest, we use the formula:

$I = P \times r \times t$

where:

• $I$ is the simple interest
• $P$ is the principal (initial loan amount)
• $r$ is the annual interest rate (in decimal form)
• $t$ is the time the money is borrowed for, in years

Given:

• $P = 5616$
• Interest rate $r = 11\frac{3}{4}\% = 11.75\% = 0.1175$
• The time period is from July 1 to December 31, which is half a year or $t = \frac{6}{12} = 0.5$ years

Now, we can substitute the values into the formula:

$I = 5616 \times 0.1175 \times 0.5$

Let's calculate this.The simple interest $I$ on the loan is $329.94.

Would you like any further details or clarifications? Here are five related questions to explore this concept further:

1. What would the interest be if the loan duration was one full year?
2. How does simple interest differ from compound interest?
3. What is the total amount to be paid back at the end of the loan period?
4. How would the interest change if the rate was 10% instead of 11.75%?
5. What would happen if the loan was extended for another six months?

Tip: Always express interest rates as decimals in calculations by dividing the percentage by 100.