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A family pays $800 per year for an insurance plan that pays 80 percent

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A family pays $800 per year for an insurance plan that pays 80 percent [#permalink]

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New post 14 Feb 2016, 05:15
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A family pays $800 per year for an insurance plan that pays 80 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total.

A $1,000
B $1,200
C $1,400
D $1,800
E $2,200

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Re: A family pays $800 per year for an insurance plan that pays 80 percent [#permalink]

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New post 14 Feb 2016, 11:06
Upfront payment for insurance plan = 800$
Family needs to pay 20 % of first 1000 $ in expense = 200$
Total amount paid by family when medical expenses are equal to or greater than 1000 $ = 800 + 200 = 1000 $
Total amount paid by insurance plan for first 1000 $ = 800 $
Total amount paid by family will equal amount paid by plan when medical expense = 1200 $
(Since insurance plan will pay 100% of amount that exceeds 1000$ )
Answer B
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Re: A family pays $800 per year for an insurance plan that pays 80 percent [#permalink]

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New post 15 Aug 2017, 11:01
Bunuel wrote:
A family pays $800 per year for an insurance plan that pays 80 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total.

A $1,000
B $1,200
C $1,400
D $1,800
E $2,200


If we let m = total medical expenses incurred by the family and p = total amount paid by family, then p = 800 + 0.2m if m ≤ 1000, or p = 800 + 0.2(1000) = 1000 if m > 1000.

If we let n = total amount paid by the insurance plan, then n = 0.8m if m ≤ 1000, or n = 0.8(1000) + m - 1000 = m - 200 if m > 1000.

We need to determine when n = p. We have two cases: 1) if m ≤ 1000; 2) if m > 1000.

1) If m ≤ 1000, we have:

n = p

0.8m = 800 + 0.2m

0.6m = 800

m = 800/0.6 = 8000/6

We see that m > 1000, which is contradictory to our assumption that m ≤ 1000. So, let’s analyze case 2.

2) if m > 1000, we have:

n = p

m - 200 = 1000

m = 1200

We see that m = 1200 is within our assumption that m > 1000. So, if the family’s total medical expenses are $1,200, then the family and the insurance company will have paid equal amounts.

Answer: B
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Re: A family pays $800 per year for an insurance plan that pays 80 percent [#permalink]

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New post 15 Aug 2017, 21:14
Initially, the total cost of the insurance paid by the family is 800$
This ensures 80% return on the first 1000$ paid for medical expenses and 100% on the remainder of the expense.

Since we need to find that amount when the price paid by the family is equal to the amount reimbursed after making expenses.
When the expense reimbursed is 800$, the actual expense is 1000$ which means that the family will pay 200$ extra.
In order to find that amount, where the cost of premium = expenses reimbursed we need another 200$ on medical expenses.
This happens when the medical expenses is 1200$(Option B)
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Re: A family pays $800 per year for an insurance plan that pays 80 percent   [#permalink] 15 Aug 2017, 21:14
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