Simple and Compound Interest

Lesson Plan -- Simple and Compound Interest

Chapter Resources - Lesson 4-14 Simple Interest - Lesson 4-14 Simple Interest Answers - Lesson 4-15 Compound Interest - Lesson 4-15 Compound Interest Answers

1 54 ok4 Ratios,Rates, Proportions, andPercents Book 4 Math Intervention Name Gr. 7NS1.7: Gr. 6NS1.4: and compound and compound and and proﬁcommissions, t markups, discounts, problems involve that tips. earned, interest at sales, discounts involving problems quantities and of percentages given 3FNFNCFS Example 1, is thevaluefor The decimalresult a fraction years fortime,create turning monthsinto in ayear. There are12months 1.5 years. 4-14 opt simple compute LESSON Standards California ——————————————————————— Solve Calculate When

month }

} 18 12 12 solve interest = and t .In . . annual interest. How muchinterest willDianna after earn as ANSWER In thesimpleinterest timeismeasured formula, in years. Write Solution Dianna deposits$ Getting Started Time: Annual rate: T

decimals. You willusethatskillinthislessontoﬁ ;QUXTM1V\MZM[\ 1. Simple interest formula: borrowed, formoneydeposited orearn Annual Interest Rate: The percent ofinterest thatyou payformoney onadeposit amount ofmoneythatyou earn Interest: The amountofmoneythatyou paytoborrow moneyorthe Balance: The sumoftheprincipal interest rate asadecimal,and outwith, ortheamountofmoneythatyou start principal E :A I I I } 12 18 Words toRemember Principal: 5 5 5 I @)584- , or 5 5 Prt $25.01 (725)(0.023)(1.5) <01; 1.5 4 Dianna will earn Dianna willearn yas Time: years years. Write theannualinterest rate asadecimal. $550 + Find theamount ofinterestearned. 7% 725 ComputingSimpleInterestEarned In how Lesson4-9you learned percents towrite as intoasavingsaccountthatpays + I $25.01 5 Multiply. Substitute $725for Use theformulaforsimpleinterest. Prt

t isthetimeinyears. where ininterest. P andtheinterest 2. Date Principal: Annual rate: I I istheinterest earned, 5 5 30 P nd simpleinterest. , 0.023for months ———————————— $870 + 3 Prt. . 7% 2 . 3% r r 18 + , and1.5for istheannual simple months? 18 P months is the t .

Copyright © by McDougal Littell, a division of Houghton Mifﬂ in Company. Copyright © by McDougal Littell, a division of Houghton Mifﬂ in Company. Name 3FNFNCFS years. must beexpressedin remember thattime simple interest.Also, when computing rates intodecimals Turn allinterest ——————————————————————— ANSWER ANSWER Write Solution You deposit Balance Solution Josh borrowed $ Time: Annual rate: Find theamountofinterest paid. T pay herbackin interest. Find youraccountbalanceafter9months. annual interest isthesum oftheprincipal money intheaccount. The will Josh pay? 5. 3. E E :A A I I I

5 You deposit Principal: 5 5 5 interest. Find your account balance after @)584- @)584- 5 5 5 $750 9 ( Prt 309 300 P 300 250 monthsas <01; 1 When an account earns interest, Whenanaccountearns theinterest isaddedtothe 2 Josh willpayhismom Your account balanceafter )( 1 Prt 1 . 5 $300 0.03 (300)(0.04)(0.75) 9 yas Time: years $335 1 $800 250 5 )( yearwith inasavingsaccountthatpays4%simpleannual . } 12 2% 1 9 ComputingSimpleInterestPaid Findingthe Balance ) from his mother to buy an electric scooter. from hismothertobuyanelectric Josh will year, or inasavingsaccountthat pays Multiply. Substitute $250for Use theformulaforsimpleinterest. balance 3 % simpleannualinterest. How muchinterest 0.75

$7.50 A year. Add. Multiply. for Substitute $300for Write thebalanceformula. 5 A 4. of an account that earns simple ofanaccountthatearns P 9 Principal: Annual rate: t . ininterest. monthsis Date 1 ok4 Ratios,Rates, Proportions, andPercents Book 4 Prt P andtheinterest P 15 42 , 0.03for months. months $1225 $309 ———————————— 8 3.2% . 3% P . r , 0.04for , and1for simpleannual Prt Math Intervention . r , and0.75 t . 55 56 ok4 Ratios,Rates, Proportions, andPercents Book 4 Math Intervention Time: Annual 15. rate: Time: Annual 13. rate: Time: Annual 11. rate: Time: Annual rate: Time: Annual rate: Time: Annual rate: Write thegiven asafractionofyear. time period 8ZIK\QKM Name Find thesimpleinterest earned. Find thesimpleinterest paid. Find thebalanceofaccount. 9. 7. 5. 3. 1. Use theformula Finding theBalance Use theformula Computing Simple Interest principal andtheinterestprincipal earned. borrow, paid, the timeinyears. Summarize Principal: Principal: Principal: Principal: Principal: Principal: 21 4 months______——————————————————————— months______P represents ortheamountthatyou depositor theprincipal 30 15 2 42 3 5 r represents theinterest rate asadecimal,and yas Time: Time: years Time: years years mnh Time: months mnh Time: Time: months months $1200 $135 $800 $200 $345 $350 4% 1.9% 4.3% 2.56% 3% 5.5% A I 5 5 Prt P 1 where Prt where I represents theinterest or earned A represents thesumof 16. 14. 12. 10. 2. 8. 6. 4. Principal: Principal: Principal: Principal: Principal: Principal: Annual rate: Annual rate: Annual rate: Annual rate: Annual rate: Annual rate: 6 32 months______months______t represents Date 2.5 18 8 10 54 3.3 years months years months years years $1580 $1020 $600 $2575 $850 $575 3.75% 4.1% 6.2% 8.2% 5.1% 2.6% ————————————

Copyright © by McDougal Littell, a division of Houghton Miffl in Company. Copyright © by McDougal Littell, a division of Houghton Miffl in Company. 20. 19. 18. 17. Explain youranswer. Write therateasadecimal. Then fi Name 22. 21. Michael borrowed Anna deposited Victor Victor deposited Tameka borrowed the moneybackin annual interest. In ______will Michael payback? ______will Tameka payininterest? 30 annual interest. If keeps themoneyinaccountfor Victor ______back in ——————————————————————— the moneyinaccountfor formula formula Find thebalanceofaccount. Fill inthemissingwords. ______have inheraccountafter2 years? an accountthatpays in years. annual interest rate asa______,and written months, how muchinterest willheearn? 18 I monthswithsimpleinterest of 5 Prt $460

$2350 where $300 $375 5 1 years, how muchinterest didAnnaearn? year at intoasavingsaccountthatpays 3.7% inasavingsaccountthatpays P tobuyadigitalmusicplayer. She willpay foranewbicycle. He willpaythemoney standsfor______, 5% simpleannualinterest. If shekeeps To ﬁ To nd theamountofsimpleinterest. 2 simpleinterest. How muchmoney years, how muchwillBelinda ,1,A7=/-<1<' nd simpleinterest you usethe Belinda deposits 5.7% . How muchinterest t standsfor______r stands for standsfor Date 3.2% 4.5% ok4 Ratios,Rates, Proportions, andPercents Book 4 $550 simple simple in ———————————— Math Intervention 57 Answer Key

Lesson 4-14, pp. 54–57 Try this: 1. 550; 0.07; 4; $154.00

2. 870; 0.037; 2.5; $80.48

3. $43.55

4. $355.86

5. $832.00

Practice: 1 1. } year 3 1 2. } year 2 7 3 3. Sample answer: } or 1 } years 4 4 8 2 4. Sample answer: } or 2 } years 3 3 5. $14.51 6. $49.34 7. $114.00 8. $195.08 9. $42.00

10. $2111.50

11. $66.41

12. $297.60

13. $212.00

14. $1082.73

15. $825.60

16. $1728.13

17. 0.032; $73.60; Sample answer: 460 3 0.032 3 5 5 73.6

18. 0.057; $32.06; Sample answer: 375 3 0.057 3 1.5 5 32.06

19. 0.05; $15.00; Sample answer: 300 3 0.05 3 1 5 15

20. 0.045; $264.38; Sample answer: 2350 3 0.045 3 2.5 5 264.38

21. principal; decimal; time

22. $590.70 58 ok4 Ratios,Rates, Proportions, andPercents Book 4 Math Intervention Name justify their reasoning. their justify solve problems and Also included: Gr. 1/2MR2.0: Gr. 7NS1.7: and and and proficommissions, t markups, discounts, problems involve that Gr. 3/4/5/6/7 MR 2.2 2.2 MR 3/4/5/6/7 Gr. 1.3; MR 6/7 Gr. and 1.2 MR fi is thebalanceof for thesecondyear In step2,theprincipal 5BLF/PUF rst year. 4-15 compound interest compute LESSON Standards California ——————————————————————— Solve simple Students Gr. 3/4/5 Gr. 3/4/5 . ;\MX Solution annually. isthebalanceofSimon’sWhat accountattheendof2years? Simon deposits$ Getting Started ANSWER ;\MX lesson you will learn howlesson you willlearn tofi or thetotalamountofinterest orpaidover earned oftime. aperiod In this +WUXW]VL1V\MZM[\ Compound interest formula: interest previously. thathasbeenearned Compound interest: Interest andany onboththeprincipal thatisearned Balance: andtheinterestThe sumoftheprincipal principal, principal, amount ofmoneyintheaccountatendtimeperiod, E

Words toRemember @)584-

The balanceattheendofﬁ Find Find Simon has Balance Balance

I I 5 5 5 5 5 5 thebalanceatendofsecondyear. thebalanceatendofﬁ r istheannualinterest rate, and Prt 12 (400)(0.03)(1) 12.36 (412)(0.03)(1) Prt

400 5 5 5 5 5 5

In how Lesson4-14you learned toﬁ 400 424.36 412 412 P P Simple Interest Computing CompoundInterestusing $424.36 inanaccountthatpays3%interest compounded 1 1 Prt Prt 1 1 12.36 12

nd compoundinterest usingthesemethods. inhisaccountafter A 5 Use thebalanceformula. Use thesimpleinterestformula. Use thebalanceformula. Use thesimpleinterestformula. P ( rst year is 1 Date 1 r rst year. ) t t where is thetimeinyears. $412 2 ———————————— A years. represents the . nd simpleinterest P isthe

Balance attheendofthird year is______. Balance attheendofsecondyear is______. Balance attheendofﬁ ANSWER Time: Annual rate: T Solution Jackie deposits$ T annually. How muchmoneywillJackie have inheraccountafter Balance year is______. attheendoffourth Balance attheendofthird year is______. Balance attheendofsecondyear is______. Balance attheendofﬁ 2. 3. 1. E :A :A A A A A Principal: Principal: Principal: @)584- 5 5 5 A 5 325(1.041) 325(1 P 366.64 5 5 <01; <01; ( 1 6 Jackie willhave 1 yas Time: years r 1 ) $850 $600 $285 t 0.041) 1

1 .%1.9% usingthesimpleinterestmethod. Find thebalanceofaccountafter usingthecompoundinterestformula. Find theamountinanaccountafter 325 3 1 , Annualrate: , Annualrate:

inanaccountthatpays Compound InterestFormula Computing CompoundInterestusingthe 3 2 $366.64

Simplify. Add. Substitute 325for Use thecompoundinterestformula. rst year is______. rst year is______. 2.4% 4% inheraccountafter , Time: , Time: Date

4. ok4 Ratios,Rates, Proportions, andPercents Book 4 Principal: Annual rate: 3 A years P 4 4 5 5 , 0.041for . years 1 % interest compounded 2 years ———————————— $1200 1 1 3 8.7% years. r 1 , and3for t years t years Math Intervention 2 3

years? t. 59 60 itrs formula. interest Find thebalanceofaccountaftertime ok4 Ratios,Rates, Proportions, andPercents Book 4 Math Intervention 6. 2. 8ZIK\QKM Name interest method. Find thebalanceof accountaftertime 9. 8. 7. 5. 4. 3. 1. an accountafter This becomes the principal foryear This becomestheprincipal Use theformula Computing Compound Interest usingtheCompound Interest Formula Compute simpleinterest for Computing Compound Interest usingSimple Interest Summarize Fill toﬁ inthemissinginformation Thebalanceforyear Thebalanceforyear Thebalanceforyear Theinterest rate asadecimalis______. written ;\MX ;\MX ;\MX Principal: $1200 $250 $135 $975 $375 $815 $435 $750 ——————————————————————— at at at at at at at foryear The principal The initialprincipal at The principal foryear The principal 5% 1.7% 4.6% 3.1% 2.3% 8.2% 4% 2.5% $600 interest compoundedannually for interest compounded annuallyfor interest compoundedannuallyfor interest compoundedannuallyfor interest compoundedannuallyfor interest compoundedannuallyfor interest compoundedannuallyfor A t interest compoundedannuallyfor , Annualrate: years. 5 P ( 1 1 r ) 1 t P to determine theamountofmoneyin todetermine 3 2 1 year. Add theinterest totheprincipal. 3 2 is______. is______. is______. is ______. 4% is______. is______. , Time: 2 nd thebalanceofaccount. . Repeat thesestepsfor t t 3 usingthecompound usingthesimple years 6 3 . years 5 10 4 4 7 2 years years 8 years years years years years Date t years. ————————————

Copyright © by McDougal Littell, a division of Houghton Mifﬂ in Company. Copyright © by McDougal Littell, a division of Houghton Mifﬂ in Company. 12. 11. 10. Solve theproblem.performed? In Exercises 12and13, how manystepsofsimpleinterest needtobe Name 14. 13. Julio deposits Solve theproblem usingthecompoundinterest Jong formula. Kim deposits after compounded annually. How muchmoneyisintheaccount ______more moneywhenhecloses hisaccount?Explain your reasoning. deposits deposits annually andkeepsthemoneyinaccountfor annually andkeepsthemoneyinaccountfor after compounded annually. How muchmoneyisintheaccount ______——————————————————————— How muchmoney is intheaccountafter ______in an account that earns in anaccountthatearns Use thecompoundinterestformula. ______. been earned onboththe______andanythathas is earned Fill inthemissingwords. 2 4 years? years? $500 $500 $650 $345 in an account that earns inanaccountthatearns inanaccountthatearns in an account that earns inanaccountthatearns in an account that earns inanaccountthatearns 2 . 4% Compound interest isinterest that interest compoundedannually. ,1,A7=/-<1<' 5 2 . . 1% 5% 5 4% years? 3 Nora deposits interest compounded interest compounded . 1% interest 2 3 interest years. Who has years. Monty Date ok4 Ratios,Rates, Proportions, andPercents Book 4 $450 ———————————— Math Intervention 61 Answer Key

Lesson 4-15, pp. 58–61

Try this: 1. $624.00; $648.96; $674.92

2. $870.40; $891.29; $912.68; $934.58

3. 285; 0.019; 6; $319.07

4. 1200; 0.087; 2; $1417.88 Practice:

1. $600; 0.04; $624.00; $624.00; $648.96; $648.96; $674.92

2. $421.82

3. $1141.46

4. $158.29

5. $282.47

6. $1462.08

7. $897.82

8. $514.87

9. $1119.15

10. 4; $389.81

11. 2; $703.04

12. Monty; Sample answer: The amount in Jong’s account is $538.45, and the amount in Monty’s account is $552.30.

13. principal; interest; previously

14. $506.65