Question
Ralph wants to purchase a renters insurance policy for his new apartment. His insurance company charges an annual premium of 16.53% of the approximate value of the items he owns and is keeping in his apartment. Below is a list of items Ralph made of the items he has in his apartment that he would like to be insured with his policy. What will Ralph’s annual renters insurance premium be?
Ralph's Stuff
Value
TV
$150
VCR
$60
DVD Player
$100
Stereo
$80
Sofa
$200
Entertainment Center
$100
Microwave
$40
Coffee Maker
$20
Computer
$850
Bicycle
$200
Coin Collection
$600
Pictures/Posters
$175
a.
$17.88
b.
$35.48
c.
$214.58
d.
$425.65
Ralph's Stuff
Value
TV
$150
VCR
$60
DVD Player
$100
Stereo
$80
Sofa
$200
Entertainment Center
$100
Microwave
$40
Coffee Maker
$20
Computer
$850
Bicycle
$200
Coin Collection
$600
Pictures/Posters
$175
a.
$17.88
b.
$35.48
c.
$214.58
d.
$425.65
Answers
GPT-4o mini
To calculate Ralph's annual renters insurance premium, we first need to determine the total value of the items he wants to insure.
Here are the values of each item:
- TV: $150
- VCR: $60
- DVD Player: $100
- Stereo: $80
- Sofa: $200
- Entertainment Center: $100
- Microwave: $40
- Coffee Maker: $20
- Computer: $850
- Bicycle: $200
- Coin Collection: $600
- Pictures/Posters: $175
Now, let's sum these values:
\[
\text{Total Value} = 150 + 60 + 100 + 80 + 200 + 100 + 40 + 20 + 850 + 200 + 600 + 175
\]
Calculating the sum:
\[
150 + 60 = 210
\]
\[
210 + 100 = 310
\]
\[
310 + 80 = 390
\]
\[
390 + 200 = 590
\]
\[
590 + 100 = 690
\]
\[
690 + 40 = 730
\]
\[
730 + 20 = 750
\]
\[
750 + 850 = 1600
\]
\[
1600 + 200 = 1800
\]
\[
1800 + 600 = 2400
\]
\[
2400 + 175 = 2575
\]
So, the total value of Ralph's items is $2575.
Next, we calculate the annual renters insurance premium by applying the rate of 16.53%:
\[
\text{Insurance Premium} = \text{Total Value} \times \text{Rate}
\]
Substituting the values we have:
\[
\text{Insurance Premium} = 2575 \times 0.1653
\]
Now, let's calculate that:
\[
\text{Insurance Premium} = 2575 \times 0.1653 \approx 426.48
\]
Based on the given options:
a. $17.88
b. $35.48
c. $214.58
d. $425.65
The closest answer to our calculation ($426.48) is option d. $425.65.
Thus, Ralph's annual renters insurance premium will be approximately **$425.65**.
Here are the values of each item:
- TV: $150
- VCR: $60
- DVD Player: $100
- Stereo: $80
- Sofa: $200
- Entertainment Center: $100
- Microwave: $40
- Coffee Maker: $20
- Computer: $850
- Bicycle: $200
- Coin Collection: $600
- Pictures/Posters: $175
Now, let's sum these values:
\[
\text{Total Value} = 150 + 60 + 100 + 80 + 200 + 100 + 40 + 20 + 850 + 200 + 600 + 175
\]
Calculating the sum:
\[
150 + 60 = 210
\]
\[
210 + 100 = 310
\]
\[
310 + 80 = 390
\]
\[
390 + 200 = 590
\]
\[
590 + 100 = 690
\]
\[
690 + 40 = 730
\]
\[
730 + 20 = 750
\]
\[
750 + 850 = 1600
\]
\[
1600 + 200 = 1800
\]
\[
1800 + 600 = 2400
\]
\[
2400 + 175 = 2575
\]
So, the total value of Ralph's items is $2575.
Next, we calculate the annual renters insurance premium by applying the rate of 16.53%:
\[
\text{Insurance Premium} = \text{Total Value} \times \text{Rate}
\]
Substituting the values we have:
\[
\text{Insurance Premium} = 2575 \times 0.1653
\]
Now, let's calculate that:
\[
\text{Insurance Premium} = 2575 \times 0.1653 \approx 426.48
\]
Based on the given options:
a. $17.88
b. $35.48
c. $214.58
d. $425.65
The closest answer to our calculation ($426.48) is option d. $425.65.
Thus, Ralph's annual renters insurance premium will be approximately **$425.65**.