The idea of insurance is that we all face risks that are unlikely but carry high cost. Think of a fire destroying your home. So we form a group to share the risk: we all pay a small armount, and the insurance policy pays a large amount to those few of us whose homes burn down. An insurance company looks at the records for millions of homeowners and sees that the mean loss from fire in a year is μ $500 per house and that the standard deviation of the loss is σ $10,000. (The distribution of losses is extremely right-skewed: most people have $0 loss, but a few have large losses.) The company plans to sell fire insurance for $500 plus enough to cover its costs and profit.

(a) Explain clearly why it would be unwise to sell only 100 policies. Then explain why selling many thousands of such policies is a safe business

(b) Suppose the company sells the policies for $600. If the company sells 50,000 policies, what is the approximate probability that the average loss in a year will be greater than $600?

answer; i believe the correct answer is (75 years);

answer; proclamation of 1763;

of the three mortgage options that demarco and tanya have to choose from, the balloon payment mortgage would be their best option, over adjustable payment and fixed payment plans.ultimately, the balloon payment plan would save demarco and tanya overall, in interest, would cost less monthly, and they would only have to make these payments for 8 years, opposing to 30 years for adjustable or fixed payment plans. 

overall, demarco and tanya would save $80,811 if they chose balloon payments over fixed payments, and would save $116,711 if they choose balloon payments over adjustable payments. benefits with choosing fixed payments over adjustable payments is that, in the end, the payments will still be $836.30 a month, while with adjustable payments, the initial monthly payments will be $763.38 to $1082.70 a month, ultimately leading to a more costly purchase. benefits with choosing fixed payments over balloon payments are not present. benefits in choosing adjustable payments over is that it has a lower interest rate, and starts with lower monthly payments initially. benefits in choosing adjustable payments over balloon payments include a lower interest rate, and lower initial monthly payments. benefits in choosing balloon payments over fixed payments include lower interest rates, lower overall price, lower monthly payments, takes less time to pay off, and does not require a downpayment. benefits in choosing balloon payments over adjustable payments include, lower monthly payments (when averaged), takes less time to pay off, and lower overall price.

hence, option c, balloon payments, is the best option for demarco and tanya to make this purchase, for it will save them a minimum of $80811, and a maximum of $116,711.