## Managing Money

Problems and tasks from a variety of sources intended to illustrate the way mathematics arises in life and work.

Rule of 72. A rule of thumb in business is that money invested at interest rate is r will double in 72/r years. Explain why this rule works, and give some examples. Use a spreadsheet to illustrate how good the rule really is.

Ordering Pizza. After studying menus from three competing pizza take-out services that offer different specials for bulk orders, decide what is the most economical order to place for a party of twenty people.

Jeans Sale. A store advertised a sale on jeans: "Buy one pair for half the price of one; or buy three pairs for the price of one. (You must pay for the most expensive pair.)" Two friends were shopping for jeans for their children. One wanted to buy six pairs-- three listed at \$45, \$24, \$20, and three listed at \$23 each; the other wanted to buy four pairs--two listed at \$55 and \$35, and two at \$28 each. Explain how these friends can combine their purchases to take best advantage of the sale.

Lottery Winnings. Suppose you win a \$1,000,000 lottery, which is to be paid in twenty annual installments of \$50,000. During these twenty years, the state authorities invest your million dollars in bonds that pay 5% per year. How much of the \$1 million does the state still have when it has finished giving you your final \$50,000 installment?

Leasing a Car. Examine the economics of buying a car vs. leasing, based on data from current newspaper advertisements.

Purchasing Insurance. After saving money for several years, you purchase a one-year old car for \$15,000. With this investment, you need collision insurance. As the deductible rises from \$100 to \$250 to \$500, the annual premiums for collision coverage decline from \$250 to \$200 to \$150. Explain how the choice of policy depends on your assessment of your risk of an accident.

Splitting the Tab. Five friends meet at a restaurant for dinner. Some have before-dinner drinks and others do not; some have dessert and others do not; some order inexpensive entrees, others choose fancier options. When the bill comes they need to decide whether to just add a tip and split it five ways, or whether some should pay more than others. Whatever they decide needs to be rounded to the nearest dollar or half-dollar (since it is unlikely that all individuals could produce exact change for more precise amounts). What is the quickest way to decide fairly how much each should pay?