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Benjamin currently pays $1,080 for his annual car insurance premium: He is in the Marines and will be deployed for the next 9 months Since his car will be used much...

Question

Benjamin currently pays $1,080 for his annual car insurance premium: He is in the Marines and will be deployed for the next 9 months Since his car will be used much less, there is less risk for the insurance company and it offers him a 66% discount for his annual premium while on deployment: What is the amount he must save each month while on deployment to be able to pay for the discounted premium? When Benjamin returns, his premium will revert to the amount prior to deployment: What will his to

Benjamin currently pays $1,080 for his annual car insurance premium: He is in the Marines and will be deployed for the next 9 months Since his car will be used much less, there is less risk for the insurance company and it offers him a 66% discount for his annual premium while on deployment: What is the amount he must save each month while on deployment to be able to pay for the discounted premium? When Benjamin returns, his premium will revert to the amount prior to deployment: What will his total premium for the year be? 3 points



Answers

Eric must pay his $p$ dollar annual insurance premium by himself. He works at a job after school.
a. Express how much he must save each month to pay this premium algebraically.
b. If he gets into a few accidents and his company raises his insurance 1$\%$ , express how much he must save each month to meet this new premium algebraically.

Okay, So Julian has the annual premium of X, which is going to be lowered or reduced by 35%. Since they have pain, 100% of it, she is going to pay 35% less or 65% of it, and so 65% as a decimal 0.6 spot. So that is what you multiply Times x to say this is your new lower annual premium. But your monthly premium is gonna be this divided by 12. So you take that total amount and divided by 12 individual payments. And so this is the amount she will have to pay for her new premium per, but

In this problem. We're diving into the world of car insurance, and we have this guy who is just bought a new car, and his insurance company has sent him some numbers to look at. So there are three things that were asked to do in this problem. First were asked to find the annual premium or his total yearly cost of insurance. Second were asked to find the semi annual premium. And lastly, we want to know how much less the semi annual premium would be without collision insurance because it's optional. So we argument some numbers to work with the help us solve this problem in the chart. On the left, you can see the numbers that the insurance company has sent, and it's divided by subcategory of insurance, and they're listed as annual premiums. So to figure out the total annual premium, we have to add all of these sub categories together. So let's go ahead and start with our fresh number, $234 for our personal injury protection. At our $266 we're bottling insurance liability. Add are $190 for property damage liability about $11 for uninsured motorist protection. Add $344 for comprehensive insurance ad $410. Where are collision insurance? And lastly, we're going to add $12 for emergency road service. Whether you add these by hand or with the calculator, you should get the grand total of $1467 for a total annual premium. So now we need to move on to finding the semi annual premium. So if we look at the word semi, that's a Latin word meaning half. So we're looking for the cost of half a year or six months. So when you go about dividing, we're cutting something in half. You're either going to divide by two or multiply by 1/2. So I'm going to take my total annual costs of my cost for the full year 1400 $67. And if I divide by two, that will give me half of my year or $733 50 cents as my semi annual premium. So that's what it would be for six months. Men are last problem is to figure out how much less the semi annual cost would be so that $733.50 without collision insurance. So if I look at my collision insurance, it's gonna and the old premium of $410. So that means if I did not include my collision insurance, I would be saving $410 a year or it would be $410 less on my total annual premium. So we're going to use the same process for our semi annual amounts. Were semi annual savings without this collision insurance. But I have to you figure out the semi annual premium for just collision first. So if I take my $410 which is just for my annual cost, and I divided by two in order to figure out my semi annual cost, I'm going to get a total of 200 $5 for half of a year. So if I am trying to figure out how much less my semi annual premium would be without collision insurance, well, I wouldn't have to spend that 200 $105 so it would be $205 less semi annually.

Okay, so this gentleman makes $42,990 per year. He has a monthly payment for a car loan. And he has a, um, auto insurance payment, Uh, 1277. All right, so it's good to know that this is a monthly and this is yearly. So the question is, um he is paid weekly, and we're seeing if one week's paycheck will cover this monthly cost and this monthly costs. So we're gonna break down this yearly cost into a monthly number. All right, so, um, first, let's find out how much he gets paid per week. So if you get paid this much per year and there are 52 weeks in a year, you will make 800 and $26.73 per week per paycheck because he gets paid weekly. The other thing we need to find out is what is the monthly cost of this? And what we see is, if it's paid this much per year, then we're gonna divide this by 12 months, and that will get us our monthly cost. This is going to be equal to $106.42 per month. The question is, does this amount here cover this and this? That's the question that's being asked here, and it looks like it does. So let's just double check to make sure we have $456 monthly for car 106.42 for, um, insurance. But the monthly version of it all right, and this is going to be equal to 500 and $62.42 which is less than his pay. So, yes, it covers it.

So for this problem, we have a little insurance company advertisement for its monthly rates and our problems says if Marissa was 35 years old, write that down. They're so 35 years old and she wants to purchase $30,000 of insurance. What is her premium gonna be? So if you look at the little chart it gives you, it's Ah, female age 35 male, age, 35 female age 45 and male age 45. So and then there's premium coverage for 30,000 and bring in coverage for 50,000. So we know that Marisol is a female and she wants to purchased $30,000 worth of coverage, and she's 35 years old. So you follow the line that says female age 35. And make sure you go over to the $30,000 worth of coverage and it tells you right there, that her she's a female. It's 35 and she wants $30,000 worth of coverage on her. Premium is gonna be $14 and 35 cents. There you go,


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