MA 111 Review for Exam 3Exam 3 (given in class on Thursday, April 15) will cover the consumer price index (ad-justing dollar amounts for inflation), interest, annuities (saving money by making monthlyinve stments), loans with repayment plans, and credit cards.Can you work each homework and worksheet problem correctly and quickly, providingexplanations and justifications, without looking at the text or your notes?Have you carefully studied the material in the text?Some practice problems:1. What does it mean to say that a certain amount of money today may b e worth moreor less in the past or in the future? Why does this make sense? Answer this questionwith a few complete sentences.2. Refer to the Consumer Price Index provided with Worksheet 3.1.(a) What is $2000 in 2010 dollars worth in terms of 1913 dollars?(b) What is $2000 in 1913 dollars worth in terms of 2010 dollars?(c) If a certain item cost $500 in 2000, but costs $600 today, what is the percentchange in the cost once you have adjusted for inflation?13. Simple Interest(a) Suppose an amount P is invested at a simple annual interest rate of R% for tyears, yielding a final amount A. Explain how to get the formula A = P (1 + rt),where r =R100.(b) How much would you have if you invested $3000 at a simple annual interest rateof 4.5% for 5 years?(c) How much must you invest at a simple annual interest rate of 4.5% to end upwith $3000 at the end of 5 years?(d) If you want to invest $3000 at a simple annual interest rate for 5 years to end upwith $4000, what must the interest rate be?(e) If you want to invest $3000 at a simple annual interest rate of 4.5% to end upwith $5000, how many years will you require?24. Compound Interest(a) Suppose an amount P is invested at an annual interest rate of R% compoundedyearly for t years, yielding a final amount A. Explain how to get the formulaA = P (1 + r)t, where r =R100.(b) Suppose an amount P is invested at an annual interest rate of R% compoundedmonthly for t years, yielding a final amount A. Explain how to get the formulaA = P (1 +r12)12t, where r =R100.(c) How much would you have if you invested $3000 at an annual interest rate of4.5% compounded yearly for 5 years?(d) How much would you have if you invested $3000 at an annual interest rate of4.5% compounded monthly for 5 years?(e) How much would you have if you invested $3000 at an annual interest rate of4.5% compounded continuously for 5 years? (Formula: A = P ert.)3(f) How much must you invest at an annual interest rate of 4.5% compoundedmonthly to end up with $3000 at the end of 5 years?(g) How much must you invest at an annual interest rate of 4.5% compounded con-tinuously to end up with $3000 at the end of 5 years?(h) Suppose you invest $3000 for one year at an annual interest rate of 5% com-pounded monthly. By what percent has your investment grown by the end of theyear? This is called the Annual Percent Yield (APY).(i) Suppose you want to invest $10,000 at an annual interest rate of 5.25% com-pounded monthly. How many full years will it take for you to have more than$20,000?45. Annuities(a) You invest $200 at the beginning of each month at an annual interest rate of 7%compounded monthly, for a period of 2 years. Explain why the amount of moneyyou will have at the end equals2001 +0.071224+ 2001 +0.071223+ 2001 +0.071222+ · · · +2001 +0.07123+ 2001 +0.07122+ 2001 +0.07121.(b) Suppose S = Aq + Aq2+ Aq3+ · · · + Aqm. Show how to get the formulaS = Aq qm− 1q − 1!(assuming q 6= 1).(c) Suppose you invest $200 at the beginning of each month at an annual interestrate of 7% compounded monthly for a period of 30 years. How much money willyou have in the end?(d) Suppose you wish to become a millionaire 40 years from now by making a monthlyinve stment of an amount A at the beginning of each month at an annual interestrate of 7% compounded monthly. How much do you need to invest each month?(e) Suppose you have the choice to either (a) invest $100 at the beginning of eachmonth for one year at an annual interest rate of 4% compounded monthly, or(b) invest all of $1200 right now for one year at an annual interest rate of 3.9%compounded monthly. What is the better choice?56. Loans. Formula:L =Aqm qm− 1q − 1!,where L is the amount of the loan, A is the monthly payment, q = 1 +r12, r =R100, R%is the annual interest rate, and m is the number of months.(a) You plan to borrow $100,000 to set up a 30-year mortgage. The bank can offeryou an annual interest rate of 4.5% compounded monthly.i. What will your monthly payment b e?ii. How much money will you end up paying in interest?(b) You want to borrow some money but realize that you can only afford to makemonthly payments of $200 each month.i. How much money can you borrow if you plan to pay it back over 5 years atan annual interest rate of 3% compounded monthly?ii. How much money will you end up paying in interest?67. Credit Cards(a) Assume that you have a credit card with the following terms:• The APR is 25.75%, but no interest is charged if you pay off your charges infull in the same month that they are made.• The minimum payment required is the interest accrued that month plus 2.5%of the rest of the balance. However, if this formula yields a minimum paymentthat is less than $25, the minimum payment will be $25.Suppose you charge a single item costing $900 and make the required minimumpayments. Fill in the following chart for the first two months:Month Interest Accrued Statement Minimum Payment