Cook Security Systems has a $37,500 line of credit, which charges an annual percentage rate of prime rate plus 4%. The starting balance on October 1 was $9,300.
On October 4 they made a payment of $1,800. On October 13 the business borrowed $2,100, and on October 19 they borrowed $4,400. If the current prime rate is 6%, what is the new balance (in $)? (Round your answer to the nearest cent.)
$

We can solve this problem by calculating the transactions in chronological order and taking into account the line of credit’s starting balance and changes. Here's how:

### Step 1: Starting Balance on October 1
The initial balance is **$9,300**.

### Step 2: Payment on October 4
On October 4, Cook Security Systems made a payment of **$1,800**.
\[
\text{New Balance} = 9,300 - 1,800 = 7,500
\]

### Step 3: Borrowing on October 13
On October 13, the business borrowed **$2,100**.
\[
\text{New Balance} = 7,500 + 2,100 = 9,600
\]

### Step 4: Borrowing on October 19
On October 19, the business borrowed **$4,400**.
\[
\text{New Balance} = 9,600 + 4,400 = 14,000
\]

### Final Balance
After accounting for all payments and borrowings, the new balance on the line of credit is **$14,000**.

Let me know if you need further clarifications or details on how I solved it!

Here are 5 questions to expand on this topic:
1. How would the balance change if the prime rate increases by 1%?
2. How would the interest payments be calculated on this balance if it's not paid off by the end of the month?
3. What would happen if a different amount was borrowed on October 19?
4. How does the APR affect the overall cost of the borrowed amount over time?
5. How can Cook Security Systems minimize the interest charges on their line of credit?

**Tip:** It's important to track both payments and new borrowing closely when managing lines of credit, as these directly affect both cash flow and interest costs.

Cook Security Systems has a $37,500 line of credit, which charges an annual percentage rate of prime rate plus 4%. The starting balance on October 1 was $9,300. On October 4 they made a payment of $1,800. On October 13 the business borrowed $2,100, and on October 19 they borrowed $4,400. If the current prime rate is 6%, what is the new balance (in $)? (Round your answer to the nearest cent.)

Calculate the new balance for Cook Security Systems' $37,500 line of credit, factoring in payments and borrowings. This problem uses basic arithmetic and financial accounting concepts, showing how to manage credit lines effectively. Suitable for high school students in Grades 10-12.

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