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In an effort to reduce cost on auto insurance, Sophia has lowered each component of her current plan to the cheapest possible option. Sophia’s current insurance agency is Fret-No-More Auto Insurance, whose policy options are listed below. The annual premium for Sophia’s current policy is $511.31. What decrease in her annual premium will Sophia see after the change?

Fret-No-More Auto Insurance
Type of Insurance Coverage
Coverage Limits
Annual Premiums
Bodily Injury
$25/50,000
$21.35

$50/100,000
$32.78

$100/300,000
$42.10

Property Damage
$25,000
$115.50

$50,000
$142.44

$100,000
$193.78

Collision
$100 deductible
$490.25

$250 deductible
$343.33

$500 deductible
$248.08

Comprehensive
$50 deductible
$105.79

$100 deductible
$88.23
a.
$20.59
b.
$38.15
c.
$57.10
d.
$60.88

1 answer

To determine how much Sophia will save on her annual premium by opting for the cheapest possible options in each component of her auto insurance, we need to add up the premiums for the cheapest options for each type of coverage and then compare the new total to her current annual premium of $511.31.

Here are the cheapest options for each type of coverage:

  1. Bodily Injury:

    • $25/50,000: $21.35 (cheapest option)

  2. Property Damage:

    • $25,000: $115.50 (cheapest option)

  3. Collision:

    • $500 deductible: $248.08 (cheapest option)

  4. Comprehensive:

    • $100 deductible: $88.23 (cheapest option)

Now, we will add these premiums together to find the total cost of the new policy:

\[ \text{Total Premium} = \text{Bodily Injury} + \text{Property Damage} + \text{Collision} + \text{Comprehensive} \]

\[ \text{Total Premium} = 21.35 + 115.50 + 248.08 + 88.23 \]

Calculating the total:

\[ \text{Total Premium} = 21.35 + 115.50 = 136.85 \] \[ 136.85 + 248.08 = 384.93 \] \[ 384.93 + 88.23 = 473.16 \]

The total premium for the cheapest options is $473.16.

Now, let's find the decrease in Sophia's annual premium:

\[ \text{Decrease} = \text{Current Premium} - \text{New Premium} \] \[ \text{Decrease} = 511.31 - 473.16 \] \[ \text{Decrease} = 38.15 \]

Thus, the decrease in Sophia's annual premium after the change will be $38.15.

The answer is b. $38.15.