Build a Monte Carlo simulation model to show your out of pocket expenses in this situation

Your son has just gotten his driver’s license and your bank account is about to get a little (a lot?) lighter. To help mitigate the impact on your finances, you have opted for a high deductible auto insurance policy. The deductible on your policy is $4000, which means that you will pay the first $4000 of any damages and then the insurance will cover the rest. Because of this, if there is an accident for which the damanges are less than $4000, you aren’t even going to file a claim with the insurance company. The less they know, the better? You will just pay it out of pocket. You believe that any accident will result in a damage amount which is normally distributed with a mean of $4500 and a standard deviation of $1500. The value of your son’s car is only $7500, so that is the upper bound on the damage amount because in that case, you can junk the car and buy a different one for $7500. The lower bound on damages is obviously $0. The probability of an automobile accident this year is 7.5%.

Build a Monte Carlo simulation model to show your out of pocket expenses in this situation. If there is no accident, then there is no out of pocket expense.

Analyze the results of the 1000 iterations to find the following as a percentage of the 1000 iteration:

1. how often a claim was filed (damage met deductible).

2. how often you ended up buying a different car.

Also, calculate your expected out of pocket expense.