Review Miterm 2 Problems Math 1030

Transcription

1 Section C.1: Significant Digits Ex.1 Counting significant digits. State the number of significant digits and the implied meaning of the following numbers: (1) a time of 96.7 seconds; (2) a length of feet; (3) a population reported as 30, 000; (4) a population reported as Section C.2: Rounding Ex.2 Rounding with significant digits. For each of the following operations, give your answer with the specified number of significant digits: (1) 4.7 mm mm; give your answer with 2 significant digits; (2) 450, ; give your answer with 3 significant digits. 1

2 Section C.3: Understanding Errors Ex.3 Scientists studying global warming need to know how the average temperature of the entire Earth, or the global average temperature, has changed with time. Consider two difficulties (among many others) in trying to interpret historical temperature data from the early 20th century: (1) temperatures were measured with simple thermometers and the data were recorded by hand; (2) most temperature measurements were recorded in or near urban areas, which tend to be warmer than surrounding rural areas because heat released by human activity. Discuss whether each of these two difficulties produces random or systematic errors, and consider the implications of these errors. Ex.4 Find the absolute and relative error in each case. (1) Your true weight is 160 pounds, but a scale says you weigh 162 pounds. (2) The government claims that a program costs $13.0 billion, but an audit shows that the true cost is $10.0 billion. 2

3 Ex.5 Accuracy and Precision in your Weight. Suppose your true weight is pounds. The scale at the doctor s office, which can be read only to the nearest quarter pound, says that you weigh pounds. The scale at the gym, which gives a digital readout to the nearest 0.1 pound says that you weigh Which scale is more precise? Which scale is more accurate? 3

4 Section C.3: Combining Measured Numbers Ex.6 Suppose that you live in a city with a population of 40, 000. One day, your 15 friends move to your city. What is the population of your city now? Section D.1: What Is an Index Number? Ex.7 Finding an index number. The price of gasoline in 1985 was cents. Using the 1975 price (= 56.7 cents) as the reference value, find the price index number for gasoline in

5 Making Comparisons with Index Numbers Ex.8 Suppose it cost $7.00 to fill a gas tank in How much would it have cost to fill the same tank in 2003? (price index for 2005 = 184, reference value = 1975 price). Ex.9 Suppose the current price of gasoline is $3.20 per gallon. Using the 1985 price (= $1.196) as the reference value, find its price index number. 5

6 Section D.2: The Consumer Price Index Ex.10 To find out how much higher typical prices were in 2003 than in 1995, compute the ratio of the CPIs for the two years using the shorthand CPI 2003 to represent the CPI for 2003 and the shorthand CPI 1995 to represent the CPI for 1995: Ex.11 Find the rate of inflation from 1974 to 1975 (CPI 1974 = 49.3, CPI 1975 = 53.8). Ex.12 According to computer performance tests, a Macintosh computer that cost $900 in 2005 had computing power equivalent to that of a supercomputer that sold for $30 million in If computer prices had risen with inflation, how much would the computing power of the 1985 supercomputer have cost in 2005? What does this tell us about the cost of computers? 6

7 Section B.1: Simple versus Compound Interest Ex.13 Savings bond. While banks almost always pay compound interest, bonds usually pay simple interest. Suppose you invest $5000 in a savings bond that pays simple interest of 12% per year. How much total interest will you receive in 5 years? If the bond paid compound interest would you receive more or less total interest? Explain. Section B.2: Compound Interest Formula Ex.14 Simple and compound interest. You invest $200 in two accounts that each pay an interest rate of 12% per year. However, one account pays simple interest and one account pays compound interest. Make a table that shows the growth of each account over a 3 year period. Use the compound interest formula to verify the result in the table for the compound interest case. 7

8 Section B.4: Compound Interest Paid More Than Once a Year Ex.15 You deposit $2000 in a bank account that pays an APR of 5% and compound interest monthly. How much money will you have after 12 years? Compare this amount to the amount you would have if interest were paid only once per year. Section B.5: Annual Percentage Yield (APY) Ex.16 You deposit $2000 into an account with APR = 4%. Find the annual percentage yield with monthly compounding and with daily compounding. 8

9 Section B.6: Continuous Compounding Ex.17 You deposit $150 in an account with an APR of 7% and continuous compounding. How much will you have after 15 years? Section B.7: Planning Ahead with Compound Interest Ex.18 Suppose you could make a single deposit in an investment with an interest rate of APR = 7%, compounded annually, and leave it there for the next 20 years. How much would you have to deposit now to realize $200, 000 after 20 years? 9

10 Section C.1: The Savings Plan Formula Ex.19 Suppose you deposit $2500 into your savings plan at the end of each month. Further, suppose that your plan pays interest monthly at an annual rate of AP R = 24%, or 2% per month. What is your balance at the end of 15 months? 10

11 Section C.2: Planning Ahead with Savings Plans Ex.20 You want to build a $180, 000 college fund in 18 years by making a regular, end-of-month deposits. Assuming an AP R of 8%, calculate how much you should deposit monthly. How much of the financial value comes from actual deposits and how much from interest? 11

12 Section C.3: Total Return Ex.21 Consider a case in which you invest a starting principal of $1, 500 and it grows to $3, 800 in 14 years. Calculate the total return. Section D.1: Loan Basics Ex.22 Student loan. Suppose you have student loans totaling $6000 when you graduate from college. The interest rate is APR = 10% and the term is 8 years. What are your monthly payments? How much will you pay over the lifetime of the loan? What is the total interest you will pay on the loan? 12

13 Ex.23 You need a $8000 loan to buy a used car. Your bank offers a 3-year loan at 7.2%, a 4-year loan at 8.5%, and a 5-year loan at 9%. Calculate your monthly payments and total interest over the loan term with each option. 13

14 Section D.2: Credit Cards Ex.24 You have a credit card balance of $2900 with an annual interest rate of 20%. You decide to pay off your balance in 1 year. How much will you need to pay each month? Assume you make no further credit card purchases. 14

15 Section D.3: Mortgages Ex.25 You need a loan of $250, 000 to buy your new home. The bank offers a choice of a 30-year loan at an APR of 9% or a 15-year loan at 7%. Compare your monthly payments and total loan cost under the two options. Assume that the closing costs are the same in both cases and therefore do not affect the choice. 15