When cars made by General motors in the USA started bursting into flames on being hit in the rear, burning the occupants to death, a couple of General Motors executives sat down to a restaurant meal and worked out the cheapest way to solve the problem.
Their solution was not to work out the cheapest way to redesign the car in question to make it safe. They worked out instead that it would be cheaper to compensate any unlucky survivors and pay their medical bills than pay to redesign the model and recall all the affected cars to be made safe. Their calculations went something like this:
One million recalls and rectifications at $500 each equals $500,000,000.
If one person or family needed to be compensated every year, costing $1,000,000 each, at a discount rate (interest rate) of 5%, then the present value of all future compensation is
The above expression is a geometric series with first term
The sum of the series is
It is cheaper to let people burn to death in the cars sold to them by General Motors than spend money to rectify the fault.