Answered

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?




\multicolumn{3}{|c|}{Royce's Auto Insurance Policy}

Type of Insurance Coverage		Coverage LimitsAnnual 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

Verified Answer :

  • Calculate the total original premium: \(\$22.50 + \$144.75 + \$275.75 + \$100.00 = \$543.00\).
  • Apply the \(5.2\%\) increase: \(\$543.00 \times (1 + 0.052) = \$571.236\).
  • Round the result to the nearest cent: \(\$571.24\).
  • Select the matching option: \(\boxed{d}\).

Explanation

  1. Calculate the Original Total Premium

To determine Royce's new annual premium after his accident, we must first calculate the original total annual premium from the provided components in the insurance policy table. The components are:

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

The original total annual premium is the sum of these four amounts:
\[\$22.50 + \$144.75 + \$275.75 + \$100.00 = \$543.00\]

  1. Calculate the New Annual Premium

After finding the original total annual premium, we apply the \(5.2\%\) increase. This can be done by calculating the increase amount and adding it to the original total, or by multiplying the original total by \(1.052\).

The increase amount is:
\[\$543.00 \times 0.052 = \$28.236\]

The new annual premium is:
\[\$543.00 + \$28.236 = \$571.236\]

Rounding to the nearest cent, as insurance premiums are typically represented, we get \(\$571.24\). This corresponds to option d.

Examples

Insurance companies often calculate adjustments based on risk factors, such as accidents or driving records. By understanding how a percentage increase is applied to a base cost, individuals can better anticipate changes in their financial obligations. This calculation method is a foundational skill for personal finance management, budget planning, and analyzing service agreements to ensure accurate payments.

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