You have a choice of two health insurance​ plans:
timesPlan A​ (low deductible): Annual premium is ​$5400​, deductible is ​$500 ​(for the​ year), and there are no​ co-payments. The insurance plan covers​ 100% of all expenses after the deductible is met.
timesPlan B​ (high deductible): Annual premium is ​$1600​, deductible is ​$2200 ​(for the​ year), and the​ co-payments are ​$110 for an emergency room​ visit, ​$110 for radiology procedures such as CT​ scans, and ​$30 for an office visit. The insurance covers 60​% of all expenses after the deductible is met and your​ co-payments are subtracted.
Find the​ out-of-pocket expenses under each plan assuming​ that, in one​ year, you have one emergency room visit that costs ​$3500​, one annual​ check-up that costs ​$300​, and one CT scan that costs ​$800.
Question content area bottom
Part 1
The​ out-of-pocket expenses under plan A are ​$

5900.
Part 2
The​ out-of-pocket expenses under plan B are ​$

enter your response here

Let's break down the costs for each plan to calculate the out-of-pocket expenses.

### Plan A (Low Deductible)
- **Annual Premium**: $5400
- **Deductible**: $500
- After the deductible is met, Plan A covers 100% of all expenses.

For the given scenario, we have:
- **Emergency Room Visit**: $3500
- **Annual Check-up**: $300
- **CT Scan**: $800

1. **Total Medical Expenses**:  
   \[
   3500 \text{ (ER visit)} + 300 \text{ (check-up)} + 800 \text{ (CT scan)} = 4600
   \]
2. **Out-of-Pocket under Plan A**:
   - You pay the **deductible** of $500.
   - After that, Plan A covers 100% of the remaining $4100 ($4600 - $500).
   - So, the total **out-of-pocket expenses** for the medical costs are $500.
3. **Total Out-of-Pocket for Plan A**:
   - Annual Premium: $5400
   - Out-of-pocket expenses for the deductible: $500
   \[
   5400 + 500 = 5900
   \]

Thus, the total out-of-pocket expenses for **Plan A** are **$5900**.

### Plan B (High Deductible)
- **Annual Premium**: $1600
- **Deductible**: $2200
- Co-payments:
  - Emergency Room Visit: $110
  - CT Scan: $110
  - Office Visit: $30 (though it's covered under the check-up)

Plan B covers 60% of all expenses after the deductible is met and co-payments are subtracted.

1. **Emergency Room Visit**: $3500  
   You pay the **co-payment** of $110, and the rest counts toward your deductible.

2. **CT Scan**: $800  
   You pay the **co-payment** of $110, and the rest counts toward your deductible.

3. **Annual Check-up**: $300  
   Since Plan B does not mention specific coverage for a check-up, this likely counts as an **office visit** with a co-payment of $30.

Total medical expenses before deductible:
\[
3500 + 300 + 800 = 4600
\]
Total co-payments:
\[
110 \text{ (ER visit)} + 110 \text{ (CT scan)} + 30 \text{ (check-up)} = 250
\]

4. **Deductible and Medical Coverage**:
   - You pay up to the deductible of $2200 first. The remaining amount after the deductible will be covered at 60%.
   - Medical costs after co-payments:
     \[
     4600 - 250 \text{ (co-payments)} = 4350
     \]
     The first $2200 of this amount goes toward the deductible, leaving:
     \[
     4350 - 2200 = 2150
     \]
     Now, 60% of this $2150 is covered by insurance:
     \[
     0.60 \times 2150 = 1290
     \]
     So, you pay 40% of the remaining $2150:
     \[
     0.40 \times 2150 = 860
     \]

5. **Total Out-of-Pocket for Plan B**:
   - Annual Premium: $1600
   - Deductible: $2200
   - Co-payments: $250
   - Your share of the post-deductible expenses: $860
   \[
   1600 + 2200 + 250 + 860 = 4910
   \]

Thus, the total out-of-pocket expenses for **Plan B** are **$4910**.

### Summary:
- Plan A: $5900
- Plan B: $4910

Let me know if you'd like any further breakdowns, or if you have other questions!

---

Here are five questions for deeper exploration:

1. How would the results change if there were more medical expenses throughout the year?
2. What if Plan B had a different co-insurance percentage (e.g., 80%)?
3. How does the deductible affect the choice between low- and high-deductible plans?
4. Would Plan B still be better if you had fewer medical expenses?
5. What happens if co-payments or premiums increase significantly next year?

Tip: When choosing insurance plans, consider not only premiums and deductibles but also your expected annual healthcare usage.

You have a choice of two health insurance​ plans: Plan A​ (low deductible): Annual premium is ​$5400​, deductible is ​$500 ​(for the​ year), and there are no​ co-payments. The insurance plan covers​ 100% of all expenses after the deductible is met. Plan B​ (high deductible): Annual premium is ​$1600​, deductible is ​$2200 ​(for the​ year), and the​ co-payments are ​$110 for an emergency room​ visit, ​$110 for radiology procedures such as CT​ scans, and ​$30 for an office visit. The insurance covers 60​% of all expenses after the deductible is met and your​ co-payments are subtracted. Find the​ out-of-pocket expenses under each plan assuming​ that, in one​ year, you have one emergency room visit that costs ​$3500​, one annual​ check-up that costs ​$300​, and one CT scan that costs ​$800.

Understand how to calculate the out-of-pocket expenses for two health insurance plans. This problem involves determining total costs based on premiums, deductibles, and co-payments for Plan A and Plan B, including a detailed breakdown of percentage-based calculations. Ideal for Grades 10-12.

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