614 CHAPTER 10 Consumer Mathematics compounded quarterly. In the fine print at the bottom of the advertisement, it stated that the APY on the CD was 4.58%. Was this advertisement accurate? Explain. Yes In Exercises 37– 42, round your answers up to the nearest cent. 37. Starting a New Business Corinne’s goal is to have $55,000 to start a new cake decorating business when she retires in 15 years. How much should she invest now in a CD that pays 4% interest compounded quarterly to reach her goal? $30,274.73 38. Starting a New Business Lynn’s goal is to have $26,000 to start a new lawn mower repair business when he retires in 15 years. How much should he invest now in a CD that pays 2% interest compounded quarterly to reach his goal? $19,275.68 39. A New Car Adam wishes to have $25,000 available in 18 years to purchase a new car for his son as a gift for his high school graduation. To accomplish this goal, how much should Adam invest now in a CD that pays 3.5% interest compounded quarterly? $13,351.34 40. Kitchen Remodel Diane plans to remodel her kitchen in 5 years. How much should Diane invest in a money market account that pays 2.1% interest compounded quarterly in order to have $8000 in 5 years? $7204.58 41. A New Water Tower The village of Kieler recently completed the construction of a new water tower. The entire cost of the water tower was $925,000, and the state paid $370,000 of the total cost through the awarding of a grant. In addition, the village can delay paying the balance of the cost for 30 years (without paying any interest during the 30 years). To finance the balance, the village board will at this time assess its 598 homeowners a one-time flat fee surcharge and then invest this money in a 30-year CD paying 7.5% interest compounded monthly. a) What is the balance due on the water tower? $555,000 b) How much will the village of Kieler need to invest at this time in the CD to raise the balance due in 30 years? $58,907.61 c) What amount should each homeowner pay as a surcharge? $98.51 42. After seeing its neighboring village obtain a new water tower (see Exercise 41), the city board of East Dubuque begins planning to replace its water towers. The board estimates that it will need $1,750,000 to build the new water towers in 20 years. At this time, the city board plans to assess its 2753 homeowners with a one-time flat fee surcharge and then invest the money received in a CD paying 9% interest compounded daily for 20 years. a) How much money will the board need to raise at this time to meet the city’s water tower needs at the end of the 20 years? $289,338.14 b) Before applying the surcharge, the city board receives a federal grant of $100,000 toward the water tower investment. Taking this grant into account, how much should the surcharge be on each homeowner? $68.78 Concept/Writing Exercises 43. Doubling the Rate Determine the total amount and the interest paid on $1000 with interest compounded semiannually for 2 years at a) 2%. $1040.60, $40.60 b) 4%. $1082.43, $82.43 c) 8%. $1169.86, $169.86 d) Is there a predictable outcome in either the amount or the interest when the rate is doubled? Explain. No 44. Doubling the Principal Compute the total amount and the interest paid at 12% compounded monthly for 2 years for the following principals. a) $100 $126.97, $26.97 b) $200 $253.95, $53.95 c) $400 $507.89, $107.89 d) Is there a predictable outcome in the interest when the principal is doubled? Explain. Yes, the interest also doubles. 45. Interest Comparison You are given a choice of taking the simple interest on $100,000 invested for 4 years at a rate of 5% or the interest on $100,000 invested for 4 years at an interest rate of 5% compounded daily. Which would you select? Explain your answer and give the difference in the two investments. * 46. Inflation The price of a widget this year is $1. Assuming an annual inflation rate of 3.5%, what will be the price of the widget in 5 years? $1.19 Challenge Problems/Group Activities 47. Determining the Interest Rate For a total accumulated amount of $3586.58, a principal of $2000, and a time period of 5 years, use the compound interest formula to determine r if interest is compounded monthly. 11.74% 48. Rule of 72 A simple formula can help you estimate the number of years required to double your money. It’s called the rule of 72. You simply divide 72 by the interest rate (without the percent sign). For example, with an interest rate of 4%, your money would double in approximately 72 4, ÷ or 18 years. In (a)–(d), determine the approximate number of years it will take for $1000 to double at the given interest rate. a) 3% 24 years b) 6% 12 years c) 8% 9 years d) 12% 6 years e) If $120 doubles in approximately 22 years, estimate the rate of interest. 3.27% *See Instructor Answer Appendix Blend Images/Shutterstock
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