Question
The annual insurance premium for a car Nicole bought 6 months ago is $756.00 with a $500 deductible for collision. Nicole had just paid the bill for her sixth month of insurance before she was involved in a car accident resulting in $2,000 in damage to her car. Because she had collision insurance in her policy, the insurance company took care of all of the repairs less the $500.00 deductible.
Considering how much she paid in insurance premiums and deductibles, would you say the purchase of insurance over the last 6 months was a good investment for Nicole? Why or why not?
Considering how much she paid in insurance premiums and deductibles, would you say the purchase of insurance over the last 6 months was a good investment for Nicole? Why or why not?
Answers
GPT-4o mini
To evaluate whether Nicole's purchase of insurance over the last 6 months was a good investment, we need to look at her insurance costs relative to the damages she incurred due to the accident.
1. **Total Insurance Premium Paid**:
- Nicole's annual premium is $756.
- For 6 months, she has paid:
\[
\text{Total Premium for 6 months} = \frac{756}{12} \times 6 = 378
\]
2. **Deductible**:
- Nicole has a deductible of $500 that she must pay out of pocket due to the accident.
3. **Total Out-of-Pocket Costs**:
- Incurred damages due to the accident: $2,000.
- Amount paid by insurance after the deductible:
\[
\text{Insurance Payout} = 2000 - 500 = 1500
\]
- Total out-of-pocket costs (deductible + insurance):
\[
\text{Total Cost} = \text{All Premiums} + \text{Deductible} = 378 + 500 = 878
\]
4. **Net Gain/Loss from Insurance**:
- Considering the insurance payout, Nicole received $1,500 for the repairs.
- Her total investment in insurance and deductible is $878.
5. **Analysis**:
- Insurance benefit: $1,500 (for repairs)
- Costs incurred: $878 (insurance premiums + deductible)
- Profit from insurance:
\[
\text{Profit} = \text{Insurance Payout} - \text{Total Investment} = 1500 - 878 = 622
\]
Putting all this together, Nicole benefited significantly from having insurance. She incurred a total cost of $878 for insurance and the deductible but received $1,500 for the repairs. Thus, she made a net gain of $622 from her insurance purchase.
**Conclusion**:
Yes, purchasing the insurance over the last 6 months was a good investment for Nicole. It helped her cover the majority of the repair costs after her accident, leaving her financially better off than she would have been without the insurance.
1. **Total Insurance Premium Paid**:
- Nicole's annual premium is $756.
- For 6 months, she has paid:
\[
\text{Total Premium for 6 months} = \frac{756}{12} \times 6 = 378
\]
2. **Deductible**:
- Nicole has a deductible of $500 that she must pay out of pocket due to the accident.
3. **Total Out-of-Pocket Costs**:
- Incurred damages due to the accident: $2,000.
- Amount paid by insurance after the deductible:
\[
\text{Insurance Payout} = 2000 - 500 = 1500
\]
- Total out-of-pocket costs (deductible + insurance):
\[
\text{Total Cost} = \text{All Premiums} + \text{Deductible} = 378 + 500 = 878
\]
4. **Net Gain/Loss from Insurance**:
- Considering the insurance payout, Nicole received $1,500 for the repairs.
- Her total investment in insurance and deductible is $878.
5. **Analysis**:
- Insurance benefit: $1,500 (for repairs)
- Costs incurred: $878 (insurance premiums + deductible)
- Profit from insurance:
\[
\text{Profit} = \text{Insurance Payout} - \text{Total Investment} = 1500 - 878 = 622
\]
Putting all this together, Nicole benefited significantly from having insurance. She incurred a total cost of $878 for insurance and the deductible but received $1,500 for the repairs. Thus, she made a net gain of $622 from her insurance purchase.
**Conclusion**:
Yes, purchasing the insurance over the last 6 months was a good investment for Nicole. It helped her cover the majority of the repair costs after her accident, leaving her financially better off than she would have been without the insurance.