Lesson Plan -- Simple And Compound Interest

Lesson Plan -- Simple and Compound InterestChapter Resources- Lesson 4-14 Simple Interest- Lesson 4-14 Simple Interest Answers- Lesson 4-15 Compound Interest- Lesson 4-15 Compound Interest Answers1

Name . 6 NS 1.4: Calculategiven percentages ofquantities and solveproblems involvingdiscounts at sales,interest earned, andtips.Gr. 7 NS 1.7: Solveproblems that involvediscounts, markups,commissions, and profi tand compute simpleand compound interest.Date ————————————;QUXTM 1V\MZM[\Words to RememberInterest: The amount of money that you pay to borrow money or theamount of money that you earn on a depositAnnual Interest Rate: The percent of interest that you pay for moneyborrowed, or earn for money depositedSimple interest formula: I 5 Prt where I is the interest earned, P is theprincipal or the amount of money that you start out with, r is the annualinterest rate as a decimal, and t is the time in years.Balance: The sum of the principal P and the interest Prt.Getting Started In Lesson 4-9 you learned how to write percents asdecimals. You will use that skill in this lesson to find simple interest.Computing Simple Interest EarnedDianna deposits 725 into a savings account that pays 2.3% simpleannual interest. How much interest will Dianna earn after 18 months?Solution3FNFNCFSThere are 12 monthsin a year. Whenturning months intoyears for time, createa fraction month}.12The decimal resultis the value for t. In18Example 1, } 121.5 years.In the simple interest formula, time is measured in years. Write 18 months18as }, or 1.5 years. Write the annual interest rate as a decimal.12I 5 PrtUse the formula for simple interest.I 5 (725)(0.023)(1.5)Substitute 725 for P, 0.023 for r, and 1.5 for t.I 5 25.01Multiply.ANSWER Dianna will earn 25.01 in interest.T:A 0 1;Find the amount of interest earned.1. Principal: 550Annual rate: 7%Time: 4 yearsI5 554Math InterventionBook 4 Ratios, Rates, Proportions, and Percents2. Principal: 870 Annual rate: 3.7%Time: 30 monthsI5 5Copyright by McDougal Littell, a division of Houghton Mifflin Company.E@)584-

Name �——————E@)584- Date ————————————Computing Simple Interest PaidJosh borrowed 250 from his mother to buy an electric scooter. Josh willpay her back in 1 year with 3% simple annual interest. How much interestwill Josh pay?Solution3FNFNCFSTurn all interestrates into decimalswhen computingsimple interest. Also,remember that timemust be expressed inyears.I 5 PrtUse the formula for simple interest.I 5 (250)(0.03)(1)Substitute 250 for P, 0.03 for r, and 1 for t.I 5 750Multiply.ANSWER Josh will pay his mom 7.50 in interest.Balance When an account earns interest, the interest is added to themoney in the account. The balance A of an account that earns simpleannual interest is the sum of the principal P and the interest Prt.A 5 P 1 PrtE@)584- Finding the BalanceCopyright by McDougal Littell, a division of Houghton Mifflin Company.You deposit 300 in a savings account that pays 4% simple annualinterest. Find your account balance after 9 months.Solution9Write 9 months as } year, or 0.75 year.12A 5 P 1 PrtWrite the balance formula.5 300 1 (300)(0.04)(0.75)Substitute 300 for P, 0.04 for r, and 0.75for t.5 300 1 9Multiply.5 309Add.ANSWER Your account balance after 9 months is 309.T:A 0 1;Find the amount of interest paid.3. Principal: 335Annual rate: 5.2%Time: 2.5 years4. Principal: 1225Annual rate: 8.3%Time: 42 months5. You deposit 800 in a savings account that pays 3.2% simple annualinterest. Find your account balance after 15 months.Math InterventionBook 4 Ratios, Rates, Proportions, and Percents55

Name �——————Date ting Simple InterestUse the formula I 5 Prt where I represents the interest earned orpaid, P represents the principal or the amount that you deposit orborrow, r represents the interest rate as a decimal, and t representsthe time in years.Finding the BalanceUse the formula A 5 P 1 Prt where A represents the sum of theprincipal and the interest earned.8ZIK\QKMWrite the given time period as a fraction of a year.1.4 months2.6 months3.21 months4.32 monthsFind the simple interest earned.Annual rate: 4.3%Time: 30 months7. Principal: 1200Annual rate: 1.9%Time: 5 years6. Principal: 575Annual rate: 2.6%Time: 3.3 years8. Principal: 850Annual rate: 5.1%Time: 54 monthsFind the simple interest paid.9. Principal: 350Annual rate: 4%Time: 3 years11. Principal: 345Annual rate: 5.5%Time: 42 months10. Principal: 2575Annual rate: 8.2%Time: 10 years12. Principal: 600Annual rate: 6.2%Time: 8 yearsFind the balance of the account.13. Principal: 200Annual rate: 3%Time: 2 years15. Principal: 800Annual rate: 2.56%Time: 15 months56Math InterventionBook 4 Ratios, Rates, Proportions, and Percents14. Principal: 1020Annual rate: 4.1%Time: 18 months16. Principal: 1580Annual rate: 3.75%Time: 2.5 yearsCopyright by McDougal Littell, a division of Houghton Mifflin Company.5. Principal: 135

Name �——————Date ————————————Write the rate as a decimal. Then find the amount of simple interest.Explain your answer.17. Anna deposited 460 into a savings account that pays 3.2% simpleannual interest. In 5 years, how much interest did Anna earn?18. Michael borrowed 375 for a new bicycle. He will pay the moneyback in 18 months with simple interest of 5.7%. How much interestwill Michael pay back?19. Tameka borrowed 300 to buy a digital music player. She will paythe money back in 1 year at 5% simple interest. How much moneywill Tameka pay in interest?Copyright by McDougal Littell, a division of Houghton Mifflin Company.20. Victor deposited 2350 in a savings account that pays 4.5% simpleannual interest. If Victor keeps the money in the account for30 months, how much interest will he earn?,1, A7 / - 1 '21. Fill in the missing words. To find simple interest you use theformula I 5 Prt where P stands for , r stands forannual interest rate written as a , and t stands forin years.22. Find the balance of the account. Belinda deposits 550 inan account that pays 3.7% simple annual interest. If she keepsthe money in the account for 2 years, how much will Belindahave in her account after 2 years?Math InterventionBook 4 Ratios, Rates, Proportions, and Percents57

Answer KeyLesson 4-14, pp. 54–57Try this:1. 550; 0.07; 4; 154.002. 870; 0.037; 2.5; 80.483. 43.554. 355.865. 832.00Practice:11. }  3 year12. }  2 year733. Sample answer:  } or 1  } years44824. Sample answer:  } or 2  } years335. 14.516. 49.347. 114.008. 195.089. 42.0010. 2111.5011. 66.4112. 297.6013. 212.0014. 1082.7315. 825.6016. 1728.1317. 0.032; 73.60; Sample answer: 460 3 0.032 3 5 5 73.618. 0.057; 32.06; Sample answer: 375 3 0.057 3 1.5 5 32.0619. 0.05; 15.00; Sample answer: 300 3 0.05 3 1 5 1520. 0.045; 264.38; Sample answer: 2350 3 0.045 3 2.5 5 264.3821. principal; decimal; time22. 590.70

Name . 7 NS 1.7: Solveproblems that involvediscounts, markups,commissions, and profi tand compute simpleand compound interest.Gr. 1/2 MR 2.0: Studentssolve problems andjustify their reasoning.Also included: Gr. 3/4/5Date ———————————— WUXW]VL 1V\MZM[\Words to RememberCompound interest: Interest that is earned on both the principal and anyinterest that has been earned previously.Compound interest formula: A 5 P(1 1 r)t where A represents theamount of money in the account at the end of the time period, P is theprincipal, r is the annual interest rate, and t is the time in years.Balance: The sum of the principal and the interestMR 1.2 and Gr. 6/7 MR 1.3;Gr. 3/4/5/6/7 MR 2.2Getting Started In Lesson 4-14 you learned how to find simple interestor the total amount of interest earned or paid over a period of time. In thislesson you will learn how to find compound interest using these methods.Computing Compound Interest usingSimple InterestSimon deposits 400 in an account that pays 3% interest compoundedannually. What is the balance of Simon’s account at the end of 2 years?Solution;\MX Find the balance at the end of the first year.Use the simple interest formula.I 5 Prt5 (400)(0.03)(1)5 12Balance 5 P 1 PrtUse the balance formula.5 400 1 125 412The balance at the end of the first year is 412.;\MX Find the balance at the end of the second year.5BLF /PUF In step 2, the principalfor the second yearis the balance of thefirst year.58Use the simple interest formula.I 5 Prt5 (412)(0.03)(1)5 12.36Balance 5 P 1 PrtUse the balance formula.5 412 1 12.365 424.36ANSWER Simon has 424.36 in his account after 2 years.Math InterventionBook 4 Ratios, Rates, Proportions, and PercentsCopyright by McDougal Littell, a division of Houghton Mifflin Company.E@)584-

Name �——————T:A 0 1;Date ————————————Find the balance of the account after t yearsusing the simple interest method.1. Principal: 600, Annual rate: 4%, Time: 3 yearsBalance at the end of the first year is .Balance at the end of the second year is .Balance at the end of the third year is .2. Principal: 850, Annual rate: 2.4%, Time: 4 yearsBalance at the end of the first year is .Balance at the end of the second year is .Balance at the end of the third year is .Balance at the end of the fourth year is .E@)584- Computing Compound Interest using theCompound Interest FormulaCopyright by McDougal Littell, a division of Houghton Mifflin Company.Jackie deposits 325 in an account that pays 4.1% interest compoundedannually. How much money will Jackie have in her account after 3 years?SolutionA 5 P(1 1 r)tUse the compound interest formula.A 5 325(1 1 0.041)3Substitute 325 for P, 0.041 for r, and 3 for t.A 5 325(1.041)3Add.A 5 366.64Simplify.ANSWER Jackie will have 366.64 in her account after 3 years.T:A 0 1;Find the amount in an account after t yearsusing the compound interest formula.3. Principal: 2854. Principal: 1200Annual rate: 1.9%Time: 6 yearsA 5511 1Annual rate: 8.7%Time: 2 years2A 511 125Math InterventionBook 4 Ratios, Rates, Proportions, and Percents59

Name �——————Date ting Compound Interest using Simple InterestCompute simple interest for 1 year. Add the interest to the principal.This becomes the principal for year 2. Repeat these steps for t years.Computing Compound Interest using the Compound Interest FormulaUse the formula A 5 P(1 1 r)t to determine the amount of money inan account after t years.8ZIK\QKM1. Fill in the missing information to find the balance of the account.Principal: 600, Annual rate: 4%, Time: 3 years ;\MX The initial principal P is .The interest rate written as a decimal is .The balance for year 1 is . ;\MX The principal for year 2 is . ;\MX The principal for year 3 is .The balance for year 3 is .Find the balance of the account after time t using the simpleinterest method.2. 375 at 4% interest compounded annually for 3 years3. 975 at 8.2% interest compounded annually for 2 years4. 135 at 2.3% interest compounded annually for 7 years5. 250 at 3.1% interest compounded annually for 4 yearsFind the balance of the account after time t using the compoundinterest formula.606. 1200 at 2.5% interest compounded annually for 8 years7. 750 at 4.6% interest compounded annually for 4 years8. 435 at 1.7% interest compounded annually for 10 years9. 815 at 5% interest compounded annually for 6.5 yearsMath InterventionBook 4 Ratios, Rates, Proportions, and PercentsCopyright by McDougal Littell, a division of Houghton Mifflin Company.The balance for year 2 is .