06 03 015 1 g. you want to store the value ’ 45

McGraw-Hill Ryerson© Interest Compound Interest 8 8 8 8 If you compounded 100 for 3 years at 6 annually, semi annually, or quarterly , what are the final amounts that you would have at the end of the three 3 years ? - Future Value Annual Annual FV A = 100

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3 119.10 1 19 . 10 Semi- Semi- FV S = 100

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6 119.41 1 19 . 41 Semi = 6 2 Quarterly Quarterly FV Q = 100

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12 119.56 1 19 . 56 Quarterly = 6 4 McGraw-Hill Ryerson© Interest Compound Interest 8 8 8 8 F u tu re V al u e S o r F V F u tu re V al u e S o r F V 1 2 3 4 5 6 7 8 9 10 11 50 100 150 200 250 FV = PV 1+ i n TimeYears S= P 1+ r t Original Principal Original Principal Interest on Original Principal Interest on Interest - Future Value The Components of the Future Value of 100 McGraw-Hill Ryerson© Interest Compound Interest 8 8 8 8 Comparisons Comparisons McGraw-Hill Ryerson© Interest Compound Interest 8 8 8 8 Al Jones deposited 1,000 in a savings account for 5 years at 10 p.a.. Al Jones deposited 1,000 in a savings account for 5 years at 10 p.a.. Annual S imple I nterest Rate of 10 Annual S imple I nterest Rate of 10 Annual C ompound Rate of 10 Annual C ompound Rate of 10 Interest What is Al’s S imple I nterest and M aturity V alue? What is Al’s S imple I nterest and M aturity V alue? What is Al’s I nterest and C ompounded V alue? What is Al’s I nterest and C ompounded V alue? McGraw-Hill Ryerson© Interest Compound Interest 8 8 8 8 Interest FV = PV 1 + i n Formulae Formulae I = P r t I = 1,000 .10 5 = 500 FV = 1,000 + 500 = 1 , 500 FV = 1000

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5 = 1,000 1.6105 = 1 , 610.51 n = 5 1 = 5 I = FV – PV = 1 610.51 - 1000 Simple Simple Compound Compound Al Jones deposited 1,000 in a savings account for 5 years at 10 Al Jones deposited 1,000 in a savings account for 5 years at 10 = 610.51 i = .10 Compare Compare McGraw-Hill Ryerson© Interest Compound Interest 8 8 8 8 200 400 600 800 1000 1200 1400 1600 1800 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Years to Maturity , n Future Values of 100 at Various Rates of Interest Compounded Annually F uture V alues of 100 at Various Rates of Interest Compounded Annually 100 6 10 8 12 F u tu re V al u e F V F u tu re V al u e F V Interest Compound Interest 8 8 8 8 McGraw-Hill Ryerson© Interest Compound Interest 8 8 8 8 Ending Balance Ending Balance Compounding Period Compounding Period 1,000 1,000 Nominal Rates of Interest Compared 1 , 060.00 1 , 060.90 1 , 061.36 1 , 061.83 Beginning Balance Beginning Balance Nominal Rate Nominal Rate + 6 + 6 Annual Semiannual Quarterly Daily McGraw-Hill Ryerson© Interest Compound Interest 8 8 8 8 500 1000 1500 2000 2500 5 10 15 20 25 F u tu re V al u e F V F u tu re V al u e F V Time years 12 Compounded monthly F uture V alues of 100 at the same Nominal Rate b ut Different Compounding Frequencies 12 Co mp oun ded An nua lly Interest Compound Interest 8 8 8 8 100 McGraw-Hill Ryerson© Interest Compound Interest 8 8 8 8 Calculate the F uture V alue of 2,000 compounded daily for 4 years at 4.5. n = i = = 2,000 1.1972 = 2,394.41 = 2,000 1.1972 = 2 , 394.41 FV = 2000 1+ .045 365 1460 FV = PV 1 + i n Formula Formula Compounding Compounding Daily Daily Interest Interest Compounding Compounding Daily Daily Interest Interest Interest Compound Interest 8 8 8 8 4 365 = 1460 . 045 365 = 0.0001232 McGraw-Hill Ryerson© Interest Compound Interest 8 8 8 8 2394.41 .045 365 1 1460 2000 Solve FV = 2000 1+ .045 365 1460 = 2,394.41 = 2 , 394 . 41 Compounding Compounding Daily Daily Interest Interest Compounding Compounding Daily Daily Interest Interest McGraw-Hill Ryerson© Interest Compound Interest 8 8 8 8 FV = - 2394.41 4.5 2000 2,394.41 2 , 394 . 41 Set the frequency of interest compounding Set the frequency of interest compounding Step 1 Step 1 4 365 Input values into the financial keys Input values into the financial keys Step 2 Step 2 Compounding Compounding Daily Daily Interest Interest Compounding Compounding Daily Daily Interest Interest 365 Calculate the Future Value of 2,000 compounded daily for 4 years at 4.5. Calculate the F uture V alue of 2,000 compounded daily for 4 years at 4.5. McGraw-Hill Ryerson© Interest Compound Interest 8 8 8 8 You invested 6000 at 4.5 compounded quarterly . After 2 years , the rate changed to 5.2 compounded monthly . What amount will you have 4 1 2 years after the initial investment? Prepare a ‘time-line’ as part of the solution McGraw-Hill Ryerson© Interest Compound Interest 8 8 8 8 You invested 6000 at 4.5 compounded quarterly . After 2 years , the rate changed to 5.2 compounded monthly . What amount will you have 4 1 2 years after the initial investment? 2 years 4.5 years 6000 i = .045 4 FV 1 = PV 2 FV 1 = 6000 1+ .045 4 8 = 6000 1.0936 = 6 561.75 FV 2 i = . 052 12 FV 2 = = 6561.751.1385 = 7470.61 6 561.75 1+. 052 12 30 n = 2 4 = 8 n = 2.5 12 = 30 McGraw-Hill Ryerson© Interest Compound Interest 8 8 8 8 You invested 6000 at 4.5 compounded quarterly . After 2 years , the rate changed to 5.2 compounded monthly . What amount will you have 4 1 2 years after the initial investment? 6000 Set the frequency of interest compounding Set the frequency of interest compounding Step 1 Step 1 4 2 4.5 Input values into the financial keys Input values into the financial keys Step 2 Step 2 6,561.75 6 , 561.75 Using the TI BAII Plus financial calculator Using the TI BAII Plus financial calculator FV 1 = PV 2 FV 1 = PV 2 FV 2 4 6,571.75 McGraw-Hill Ryerson© Interest Compound Interest 8 8 8 8 You invested 6000 at 4.5 compounded quarterly . After 2 years , the rate changed to 5.2 compounded monthly . What amount will you have 4 1 2 years after the initial investment? 7470.61 Set the frequency of interest compounding Set the frequency of interest compounding Step 1 Step 1

2.5 12