Allie and Sarah decided that they want to purchase renters insurance for the apartment they share. They made a list of all of the items to be covered by the insurance policy, along with their estimated values. If the items to be covered total more than $3000, the insurance company charges an annual premium of 23% of the total value of the items. If the items to be covered total $3000 or less, the insurance company charges an annual premium of 20% of the total value of the items.

Question

Using the list of items Allie and Sarah provided, determine their monthly renters insurance premium.

Allie's Stuff
Sarah's Stuff
TV ($250)
Stereo ($75)
Stereo ($150)
Bicycle ($250)
CD's ($225)
CD's ($130)
DVD's ($385)
DVD's ($300)
Bicycle ($400)
IPOD ($80)
Microwave ($30)
Computer ($675)
Laptop Computer ($950)


a.
$65.00
b.
$74.75
c.
$325.00
d.
$780.00

Answer 1

First, we will calculate the total value of the items that Allie and Sarah want to cover with renters insurance.

Allie's Stuff:

• TV: $250
• Stereo: $75
• CD's: $225
• DVD's: $385
• Microwave: $30
• Computer: $675

Total for Allie's Stuff: \[ 250 + 75 + 225 + 385 + 30 + 675 = 1,640 \]

Sarah's Stuff:

• Stereo: $150
• Bicycle: $250
• CD's: $130
• DVD's: $300
• Bicycle: $400
• IPOD: $80
• Laptop Computer: $950

Total for Sarah's Stuff: \[ 150 + 250 + 130 + 300 + 400 + 80 + 950 = 2,260 \]

Total Value of Items:

Total Value = Total for Allie's Stuff + Total for Sarah's Stuff \[ 1,640 + 2,260 = 3,900 \]

Since the total value of the items ($3,900) is more than $3,000, we will use the premium rate of 23%.

Calculate the Annual Premium:

Annual Premium = 23% of Total Value \[ \text{Annual Premium} = 0.23 \times 3,900 = 897 \]

Convert to Monthly Premium:

Monthly Premium = Annual Premium / 12 \[ \text{Monthly Premium} = 897 / 12 \approx 74.75 \]

Therefore, the monthly renters insurance premium is approximately $74.75.

So, the correct answer is b. $74.75.