The Mathematics of Money

(Darren Dugan) #1

Copyright © 2008, The McGraw-Hill Companies, Inc.



  1. Brendan’s Doghouse Flowershop pays a different rate of electricity based on the time of day. For peak hours the rate is
    $0.118 per kilowatt-hour, while for off-peak use, the rate drops to $0.062 per kilowatt-hour. Last month, the shop used
    3,895 peak kilowatt-hours and 1,975 off-peak kilowatt-hours. Calculate the shop’s overall average cost per kilowatt-hour.


C. Indexes


  1. The GlobalInvestexx Canadian stock index, which is designed to refl ect the overall stock price performance of Canadian
    companies, stands at 1,404.53 right now. One year ago, this index stood at 1,233.59.


a. By what percent did this index’s value grow over the past year?
b. If I own a portfolio of Canadian stocks, what does this index tell you about how my portfolio did in the past year?
c. If Zarofi re Systems is one of the stocks included in this index, what can you say about what happened to the price
of its stock in the past year?


  1. If the GlobalInvestexx Mexican stock index stands at 4,800 and the GlobalInvestexx Australian stock index stands at
    9,600, what does this tell you about the value of Australian stocks compared to Mexican stocks?

  2. A personal fi nance magazine compiles an index of real estate prices in different markets around the country. On this
    index, St. Louis has a value of 114.98 and Seattle has a value of 184.92. If a house in St. Louis costs $162,500, how
    much would you expect a comparable house in Seattle to cost on the basis of these index values?

  3. A personal fi nance magazine compiles an index of real estate prices in different markets around the country. On this
    index, Houston has a value of 102.39 and Buffalo has a value of 91.15. If a house in Houston costs $174,300, how
    much would you expect a comparable house in Buffalo to cost on the basis of these index values?

  4. A cost-of-living index lists Cleveland at 103.45 and Des Moines at 97.33. If you are making $47,500 a year in
    Cleveland, how much does this index suggest you would need to earn in Des Moines to have the same buying power?

  5. A cost of living index lists Albany at 114.43 and Pittsburgh at 104.35. Right now, Sara is earning $37,340 at a job in
    Pittsburgh. If she is offered a new job in Albany paying $40,000, is this really a raise for her? Justify your answer.


D. Expected Values


  1. An auto insurer expects, from past experience, that 4 out of every 100 auto liability policies it sells will have a claim in
    the next year.


a. If the company sells 19,253 policies, what is the expected number of claims from these policies?
b. If the average claim on these policies is expected to be $22,350 per claim, what is the expected claims cost per contract?


  1. A grocery chain is offering a promotion where every 2,000th customer checking out will get his purchase for free.
    The average customer’s purchase is $98.35.


a. If the store has 6,000 customers each week, how many prizes should it expect to give away each week?
b. What is the expected cost per customer of this promotion?

Exercises 16.2 625
Free download pdf