Answered

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

Verified Answer :

  • Sum the values of all items to get a total of \(\$2,575\).
  • Convert the percentage premium rate of \(16.53\%\) to the decimal \(0.1653\).
  • Multiply the total value by the decimal rate to find the exact annual premium of \(\$425.6475\).
  • Round the result to the nearest cent to obtain the final premium of \(\boxed{\$425.65}\).

Explanation

  1. Calculating the Total Value of Items

To determine Ralph's annual renters insurance premium, we first need to find the total value of the items he intends to insure. We list the items and their respective values:

  • 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: \(\$175\)

By summing these values, we get the total value of all items:
\[150 + 60 + 100 + 80 + 200 + 100 + 40 + 20 + 850 + 200 + 600 + 175 = \$2,575\]

  1. Calculating the Annual Premium

The insurance company calculates the annual premium as \(16.53\%\) of the total value of the items. First, we convert the percentage rate into a decimal by dividing by 100:
\[16.53\% = \frac{16.53}{100} = 0.1653\]

Now, we multiply the total value of the items by this rate to find the annual premium:
\[\$2,575 \times 0.1653 = \$425.6475\]

  1. Final Calculation and Conclusion

Since monetary values are typically rounded to the nearest cent, we round \(\$425.6475\) to the nearest cent, which gives us \(\$425.65\). Ralph's total annual renters insurance premium will be \(\boxed{\$425.65}\).

Examples

Understanding how insurance premiums are calculated is a practical skill for managing personal finances. For example, if you rent an apartment and have expensive equipment, you can calculate the cost of protecting your belongings by listing their values and applying the insurance company's specific rate. This helps you budget effectively for monthly or annual expenses, ensuring you are prepared for unexpected events like theft or accidental damage. By knowing the total value of your assets, you can make informed decisions about whether the cost of a policy provides sufficient value for the coverage it offers.

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