Because of an accident Royce was involved in, his insurance company has increased his annual premium for auto insurance by 5.2%. His original policy was set up using the premiums listed below. What is his new annual premium after the increase for the accident?

Question

Royce's Auto Insurance Policy
Type of Insurance Coverage
Coverage Limits
Annual Premiums
Bodily Injury
$25/$50,000
$22.50
Property Damage
$50,000
$144.75
Collision
$500 deductible
$275.75
Comprehensive
$100 deductible
$100.00
a.
$514.76
b.
$543.00
c.
$548.20
d.
$571.24

Answer 1

To calculate Royce's new annual premium after the increase, we first need to determine his original total annual premium by adding up the premiums for each type of insurance coverage.

• Bodily Injury: $22.50
• Property Damage: $144.75
• Collision: $275.75
• Comprehensive: $100.00

Now, let's calculate the total premium:

\[ \text{Total Annual Premium} = 22.50 + 144.75 + 275.75 + 100.00 = 543.00 \]

Next, we need to apply the 5.2% increase to the total premium:

\[ \text{Increase} = \text{Total Annual Premium} \times \frac{5.2}{100} = 543.00 \times 0.052 = 28.236 \]

Now, we will add this increase to the original premium to find the new premium:

\[ \text{New Annual Premium} = \text{Total Annual Premium} + \text{Increase} \]

\[ \text{New Annual Premium} = 543.00 + 28.236 = 571.236 \]

Finally, rounding to two decimal places, the new annual premium is:

\[ \text{New Annual Premium} \approx 571.24 \]

The correct answer is \(d. , 571.24\).