Prorate the following expenses and find the corresponding monthly expense.
Lan pays a semiannual premium of ​$400 for automobile​ insurance, a monthly premium of ​$120 for health​ insurance, and an annual premium of ​$500 for life insurance.
The monthly expense is 
​(Round to the nearest cent as​ needed.)

To find the monthly expense for each type of insurance, we need to convert the semiannual and annual premiums into their monthly equivalents and add them to the already monthly expense.

1. **Automobile insurance (semiannual premium of $400):**
   - Since this is a semiannual payment, it's paid twice a year. Therefore, the monthly expense is:
     \[
     \text{Monthly expense} = \frac{400}{6} \approx 66.67
     \]

2. **Health insurance (monthly premium of $120):**
   - This is already a monthly expense, so it remains $120.

3. **Life insurance (annual premium of $500):**
   - To find the monthly cost, divide the annual premium by 12:
     \[
     \text{Monthly expense} = \frac{500}{12} \approx 41.67
     \]

4. **Total monthly expense:**
   \[
   66.67 + 120 + 41.67 = 228.34
   \]

So, the corresponding monthly expense is **$228.34**.

Would you like more details or have any questions?

Here are some related questions to expand on this topic:

1. How would the monthly expense change if the automobile insurance increased to $500 semiannually?
2. How much would Lan pay in total for all insurances annually?
3. What is the quarterly expense for each of these insurances?
4. If the health insurance premium increases by 10%, what will the new monthly expense be?
5. How would the monthly expense be affected if the life insurance is paid semiannually instead?

**Tip:** When prorating expenses, always ensure you're using the correct time period (monthly, semiannual, annual) for conversion to avoid miscalculations.

Prorate the following expenses and find the corresponding monthly expense. Lan pays a semiannual premium of ​$400 for automobile​ insurance, a monthly premium of ​$120 for health​ insurance, and an annual premium of ​$500 for life insurance. The monthly expense is ​(Round to the nearest cent as​ needed.)

Learn how to prorate insurance expenses to find the monthly cost. This example involves semiannual, monthly, and annual premiums, showing how to convert them into monthly expenses and calculate the total. Suitable for students in Grades 6-8, with key arithmetic formulas and step-by-step guidance.

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