24 CHAPTER 1 Critical Thinking Skills How Much You Withdraw Annually Affects How Long Your Money Will Last 4% 5% 6% 7% 8% 9% 10% 11 years 13 years 15 years 18 years 21 years 27 years 33 years Percent of Assets Withdrawn Annually Time Money Will Last (years) Figure 1.1 Source: NDR.com Aboatman must transport a wolf, a goat, and a bundle of herbs across a river. If the boat is so small that he can carry only one of them at a time, how can he make the crossing so that the wolf will not devour the goat and the goat will not eat the herbs? ( Clue : The boatman must make multiple round trips.) RECREATIONAL MATH Two Medieval Riddles As I was going to St. Ives, I met a man with seven wives; Every wife had seven sacks, Every sack had seven cats, Every cat had seven kits. Kits, cats, sacks, and wives, How many were going to St. Ives? The answers to these riddles are in the answer section at the back of the book. Solution a) Quite a bit of information is provided in the example. We will first need to determine what information is required to answer the question. To answer the question, we need to use only the information provided in the graph. From the graph, we can see that for assets to last 21 years, about 6% of the assets can be withdrawn annually. The amount that can be withdrawn annually is determined as follows. Amount 6% of assets Amount 0.06(500,000) 30,000 = = = Thus, about $30,000 can be withdrawn annually. b) Again, to solve this part of the example, we need only the information provided in the graph. From the graph, we can determine that if a retiree wishes for the assets to last 18 years, then 7% of the assets can be withdrawn annually. We need to determine the total assets such that 7% of the total assets is $25,000. 7% of assets $25,000 or 0.07 assets $25,000 = × = Because 0.07 is multiplied by the assets to obtain $25,000, we can determine the assets by dividing the $25,000 by 0.07 as follows. Assets 25,000 0.07 357,142.86 = ≈ Therefore, with assets of about $357,142.86, the retiree will be able to withdraw $25,000 annually and the assets will last 18 years. 7 Now try Exercise 9 Example 4 Determining a Tip The cost of Seana’s meal before tax is $28.00. a) If a 6 %1 2 sales tax is added to her bill, determine the total cost of the meal including tax. b) If Seana wants to leave a 15% tip on the pretax cost of the meal, how much should she leave? c) If she wants to leave a 20% tip on the pretax cost of the meal, how much should she leave? Solution a) The sales tax is 6 %1 2 of $28.00. To determine the sales tax, first convert 6 %1 2 to a decimal number. 6 %1 2 when written as a decimal number is 0.065. For more
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