Math

QuestionA homeowner's insurance premium of \$730 covers one year from January 12. If sold on October 23, what is the proration amount? Options: \$162.00, \$568.00, \$164.25, \$565.75.

Studdy Solution

STEP 1

Assumptions1. The insurance policy was bought on January12 and was effective through the following January11. . The premium for the policy was $730 for one year.
3. The owner decided to sell and closed escrow on October23 of the same year.
4. The policy was transferred to the new owner and prorated to the day of closing using a regular calendar year.

STEP 2

First, we need to find the total number of days the policy was in effect for the original owner. This is from January12 to October23.

STEP 3

We can calculate the number of days in each month and then add them together.January31 days -12 days (since the policy started on January12) =19 daysFebruary28 days (assuming it's not a leap year)
March31 daysApril30 daysMay31 daysJune30 daysJuly31 daysAugust31 daysSeptember30 daysOctober23 days (since the policy was transferred on October23)

STEP 4

Now, add up these days to find the total number of days the policy was in effect for the original owner.
Totaldays=19+28+31+30+31+30+31+31+30+23Total\, days =19 +28 +31 +30 +31 +30 +31 +31 +30 +23

STEP 5

Calculate the total number of days.
Totaldays=19+28+31+30+31+30+31+31+30+23=304Total\, days =19 +28 +31 +30 +31 +30 +31 +31 +30 +23 =304

STEP 6

Now, we need to find the cost of the policy per day. We can do this by dividing the total premium by the number of days in a year (365).
Costperday=Totalpremium/NumberofdaysinayearCost\, per\, day = Total\, premium / Number\, of\, days\, in\, a\, year

STEP 7

Plug in the values for the total premium and the number of days in a year to calculate the cost per day.
Costperday=$730/365Cost\, per\, day = \$730 /365

STEP 8

Calculate the cost per day.
Costperday=$730/365=$2Cost\, per\, day = \$730 /365 = \$2

STEP 9

Now that we have the cost per day, we can find the proration amount. This is the cost per day times the number of days the policy was in effect for the original owner.
Prorationamount=CostperdaytimesTotaldaysProration\, amount = Cost\, per\, day \\times Total\, days

STEP 10

Plug in the values for the cost per day and the total number of days to calculate the proration amount.
Prorationamount=$2times304Proration\, amount = \$2 \\times304

STEP 11

Calculate the proration amount.
Prorationamount=$times304=$608Proration\, amount = \$ \\times304 = \$608The proration amount is $608.

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