A stockbroker calls on potential clients from referrals. For each call, there is

Question

A stockbroker calls on potential clients from referrals. For each call, there is a 10% chance that the client will decide to invest with the firm. Fifty-five percent of those interested are found not to be qualified, based on the brokerage firm’s screening criteria. The remaining are qualified. Of these, half will invest an average of $5,000, 25% will invest an average of $20,000, 15% will invest an average of $50,000, and the remainder will invest $100,000. The commission schedule is as follows:   

Explanation / Answer

Let's say the stockbroker calls 10000 potential clients from referrals.

Hence, clients ready to invest would be = 10% = 1000

Not qualified = 55% of 100 = 550

Qualified = 450

Out of these 450 qualified investors,

Hence we can calculate :

Therefore, The commission is calculated as per different rates for different levels of investment keeping the final percentage of investors in mind.

Investment Investors % out of 10000 $5,000 0.5*450= 225 2.25 $20,000 0.25*450= 112.5 1.125 $50,000 0.15*450= 67.5 0.675 $100,000 0.10*450= 45 0.45

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