Which insurance plan is better?

[BMAD]

Mr. White and Mr. Brown work for Giant Insurance. The company offers two retirement plans, both of which are based on purchasing the company's stock. An employee can either put a fixed amount of money into his retirement plan every month to buy Giant insurance stock (plan A, which is Mr, White's choice), or buy a fixed number of Giant Insurance shares (plan B, which is Mr. Brown's choice). If there are no other fees connected with these retirement plans, which plan produces the lowest cost per share?

[jordge]

Fixed amount of money.

In both cases the average price is (total cost / number of shares)

By purchasing a fixed number of shares each period, the average price is just the average of the share price since the total cost is consistently share price times number of shares. (number of shares factors out)

By purchasing a fixed dollar amount each period, the average price becomes the 'weighted' average of the cost of the shares. Since you buy more shares when the price is low and fewer shares when the price is high, the weight shifts toward the lower cost.