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Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© 10-1 Chapter 10 O rdinary A nnuities O O A A McGraw-Hill Ryerson©

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Presentation on theme: "Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© 10-1 Chapter 10 O rdinary A nnuities O O A A McGraw-Hill Ryerson©"— Presentation transcript:

1 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© 10-1 Chapter 10 O rdinary A nnuities O O A A McGraw-Hill Ryerson©

2 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© 10-2 Calculate the… Define and distinguish between… Learning Objectives After completing this chapter, you will be able to: … Future Value and Present Value of ordinary simple annuities … ordinary simple annuities and ordinary general annuities … fair market value of a cash flow stream that includes an annuity LO-1 LO-2 LO-3

3 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© 10-3 Calculate the… Learning Objectives … Present Value of and period of deferral of a deferred annuity … principal balance owed on a loan immediately after any payment … Future Value and Present Value of ordinary general annuities LO-4 LO-5 LO-6

4 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© 10-4 Terminology - A series of equal payments at regular intervals Term of the A nnuity - the time from the beginning of the first payment period to the end of the last payment period F uture V alue P resent V alue the future dollar amount of a series of payments plus interest the amount of money needed to invest today in order to receive a series of payments for a given number of years in the future A nnuity LO-1

5 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© 10-5 Terminology … is the amount of each payment in an annuity PMT … is the number of payments in the annuity n payment interval ordinary annuities … is the time between successive payments in an annuity … are ones in which payments are made at the end of each payment interval

6 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© 10-6 Terminology Suppose you obtain a personal loan to be repaid by payment interval Term ordinary annuities 48 equal monthly payments 48 months or 4years. 1 month first payment will be due 1 month after you receive the loan, i.e. at the end of the first payment interval

7 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© 10-7 Terminology PMT 0123 nn-1 Interval number Term of the annuity Payment interval … for an n -payment Ordinary Annuity PMT

8 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© 10-8 Ordinary Annuity Ordinary S imple A nnuities Ordinary G eneral A nnuities Monthly payments, and interest is compounded monthly Monthly payments, and interest is compounded monthly Monthly payments, but interest is compounded semi-annually Monthly payments, but interest is compounded semi-annually The payment interval = the compounding interval The payment interval differs from the compounding interval The payment interval differs from the compounding interval

9 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© 10-9 $1000 $1000 (1.04) 1 n = 1 Sum = FV of annuity Interval number $1000 $1000 (1.04) 2 n = 2 $1000 (1.04) 3 n = 3 … the sum of the future values of all the payments Assume that there are four(4) annual $1000 payments with interest at 4% Future Value of an Ordinary Simple Annuity LO-2

10 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© = $ = $ FV of annuity $1000 $1000 (1.04) 1 n = 1 Sum = FV of annuity Interval number $1000 $1000 (1.04) 2 n = 2 $1000 (1.04) 3 n = 3 Assume that there are four(4) annual $1000 payments with interest at 4% $1000(1.04) +$1000(1.04) 2 +$1000(1.04) 3 = $1000 +$1040+$ $ Future Value of an Ordinary Simple Annuity

11 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Result $500 $500(1+.03/12) Sum = FV of annuity Month $500 $500(1+.03/12) 3 Suppose that you vow to save $500 a month for the next four months, with your first deposit one month from today. If your savings can earn 3% converted monthly, determine the total in your account four months from now. $500(1+.03/12) 2 $ $2, Future Value of an Ordinary Simple Annuity

12 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Now imagine that you save $500 every month for the next three years. Although the same logic applies, I certainly don’t want to do it this way! Since your ‘account’ was empty when you began… PV = 0 n = 3 yrs * 12 payments per year = 36 payments Future Value of an Ordinary Simple Annuity Using the …

13 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© You save $500 every month for the next three years. Assume your savings can earn 3% converted monthly. Determine the total in your account three years from now Future Value of an Ordinary Simple Annuity 0 12 Using the formula Note Keys direction P/Y= 120 FV =

14 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© … the sum of the future values of all the payments Future Value of an Ordinary Simple Annuity FV = PMT (1+ i) n - 1 [ i ] Formula

15 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© You save $500 every month for the next three years. Assume your savings can earn 3% converted monthly. Determine the total in your account three years from now. Future Value of an Ordinary Simple Annuity [ FV= PMT (1+ i) n - 1 i ]

16 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© You vow to save $500/month for the next four months, with your first deposit one month from today. If your savings can earn 3% converted monthly, determine the total in your account four months from now. Since your ‘account’ was empty when you began… PV = 0 n = 4 payments PMT = -500 Solving earlier Question using Annuities Solving earlier Question using Annuities

17 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Cash Flows … payments received e.g. receipts Treated as: Positives + Negatives -..a term that refers to payments that can be either … … payments made e.g. cheques Therefore…

18 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Therefore… …when you are making payments, or even making deposits to savings, Really payments to the bank! these are cash outflows, and therefore the values must be negative! Cash Flow Sign Convention Using the …

19 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© You vow to save $500/month for the next four months, with your first deposit one month from today. If your savings can earn 3% converted monthly, determine the total in your account four months from now. PV = 0 n = 4 payments PMT -500 Future Value of an Ordinary Simple Annuity FV = We already have these from before, so we don’t have to enter them again! Formula solution

20 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© You vow to save $500/month for the next four months, with your first deposit one month from today. If your savings can earn 3% converted monthly, determine the total in your account four months from now. Formula [ FV= PMT (1+ i) n - 1 i ] PMT = $500 n = 4 i =.03/12 =

21 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Not seeing the total picture! When you use formula or a calculator’s financial functions to calculate an annuity’s Future Value, the amount each payment contributes to the future value is NOT apparent!

22 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© % Compounded Annually $10.00 Years C ontribution $ $61.05 FV Contributions $10.00 FV

23 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Future Value of an Ordinary Simple Annuity You decide to save $75/month for the next four years. If you invest all of these savings in an account which will pay you 7% compounded monthly, determine: a) the total in the account after 4 years b) the amount you deposited c) the amount of interest earned Extract necessary data... PMT = = 7n = 4 * 12 = 48 - $75 PV = 0FV = ? Solve… Total Deposits = $75* 48 = $3,600 = 12

24 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© You decide to save $75/month for the next four years. If you invest all of these savings in an account which will pay you 7% compounded monthly, determine: a) the total in the account after 4 years b) the amount you deposited c) the amount of interest earned You decide to save $75/month for the next four years. If you invest all of these savings in an account which will pay you 7% compounded monthly, determine: a) the total in the account after 4 years b) the amount you deposited c) the amount of interest earned Formula solution FV……….. $4, Interest Earned = $ Deposits…... 3, P/Y = 12 FV =

25 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© FV $4, = Interest Earned $ Deposits 3, Formula [ FV= PMT (1+ i) n - 1 i ] You decide to save $75/month for the next four years. If you invest all of these savings in an account which will pay you 7% compounded monthly, determine: a) the total in the account after 4 years b) the amount you deposited c) the amount of interest earned You decide to save $75/month for the next four years. If you invest all of these savings in an account which will pay you 7% compounded monthly, determine: a) the total in the account after 4 years b) the amount you deposited c) the amount of interest earned

26 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© … the sum of the present values of all the payments PV = PMT 1-(1+ i) -n [ i ] PresentValue of an Ordinary Simple Annuity Formula

27 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© $1000 Sum = PV of annuity $1000 … the sum of the present values of all the payments Assume that there are four(4) annual $1000 payments with interest at 4% Present Value of an Ordinary Simple Annuity $1000 (1.04) -1 n = 1 $1000 (1.04) -2 n = 2 $1000 (1.04) -3 n = 3 $1000 (1.04) -4 n = Interval Number

28 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© = $ PV of annuity = $1000(1.04) -1 +$1000(1.04) -2 +$1000(1.04) -3 + = $ $ $ $ $1000 Assume that there are four(4) annual $1000 payments with interest at 4% Present Value of an Ordinary Simple Annuity $1000 (1.04) -1 n = 1 $1000 (1.04) -2 n = 2 $1000 (1.04) -3 n = 3 $1000 (1.04) -4 n = Interval Number $1000 (1.04) -4 Sum = PV of annuity

29 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Present Value of an Ordinary Simple Annuity You overhear your friend saying the he is repaying a loan at $450 every month for the next nine months. The interest rate he has been charged is 12% compounded monthly. Calculate the amount of the loan, and the amount of interest involved. … Interest - use 12, not.12 when using financial calculator … At the end of the loan, you don’t owe any money, so FV = 0 … n = 9 payments …Since you are making payments, not receiving them, PMT = Solve… … Repaid 9 payments at $450 = $4,050

30 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Formula solution You overhear your friend saying the he is repaying a loan at $450 every month for the next nine months. The interest rate he has been charged is 8% compounded monthly. Calculate the amount of the loan, and the amount of interest involved PV = 3, Amount Borrowed (PV) $ 3, Interest Paid = Repaid.…………………. 4, $

31 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Formula i PV= PMT1-(1+ i) -n [ ] - Borrowed $3, = Interest Charged $ Repaid $4, , You overhear your friend saying the he is repaying a loan at $450 every month for the next nine months. The interest rate he has been charged is 8% compounded monthly. Calculate the amount of the loan, and the amount of interest involved.

32 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Contribution of Each Payment to an Annuity’s Present Value

33 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© $10.00 Years C ontribution $ $37.91 PV Contributions $10.00 PV

34 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© …of a cash flow stream that includes an annuity Ordinary Annuities Ordinary Annuities1010 LO-3

35 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© You have received two offers on a building lot that you want to sell. Ms. Armstrong’s offer is $25,000 down plus a $100,000 lump sum payment five years from now. Mr. Belcher has offered $20,000 down plus $5000 every quarter for five years. Compare the economic values of the two offers if money can earn 5% compounded annually. LO-3

36 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© The economic value of a payment stream on a particular date (focal date) refers to a single amount that is an economic substitute for the payment stream On what information should we f ocus? WE need to choose a focal date, and determine the values of the two offers at that focal date. (Obvious choices would be today, the date of the offers, or the end of the term i.e. 5 years from now.) ocu Back to Offer Comparison

37 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Preparing Time Lines Mr. Belcher Ms. Armstrong $20,000 down plus $5000 every quarter for five years $25,000 down plus a $100,000 lump sum payment five years from now Focal Date: Today You have received two offers on a building lot that you want to sell. Ms. Armstrong’s offer is $25,000 down plus a $100,000 lump sum payment five years from now. Mr. Belcher has offered $20,000 down plus $5000 every quarter for five years. Compare the economic values of the two offers if money can earn 5% compounded annually.

38 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© $20,000 Years Time Lines $20,000 down plus $5,000 every quarter for five years $25,000 down plus a $100,000 lump sum payment five years from now A A B B $25,000 $20,000 Ms. Armstrong Mr.Belcher $5000 every quarter 5 $100,000

39 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© You have received two offers on a building lot that you want to sell. Ms. Armstrong’s offer is $25,000 down plus a $100,000 lump sum payment five years from now. Mr. Belcher has offered $20,000 down plus $5000 every quarter for five years. Compare the economic values of the two offers if money can earn 5% compounded annually. Step 1–Determine today’s value of Ms. Armstrong’s offer today’s value of lump sum 5 100, ,000 PV= , today’s value of Ms. A’s total offer Step 2… 0

40 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Step 2 – Determine today’s value of Mr. Belcher’s offer P/Y = 4C/Y = 1 0PV = 79, , today’s value of lump sum today’s value of Mr. B’s total offer You have received two offers on a building lot that you want to sell. Ms. Armstrong’s offer is $25,000 down plus a $100,000 lump sum payment five years from now. Mr. Belcher has offered $20,000 down plus $5000 every quarter for five years. Compare the economic values of the two offers if money can earn 5% compounded annually.

41 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© $103, , $ 3, Better off accepting Ms. Armstrong’s offer! Ms. Armstrong Mr.Belcher Total Value of each offer Total Value of each offer Difference in Offers

42 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© The required monthly payment on a five-year loan, bearing 8% interest, compounded monthly, is $ Since you are “borrowing” money, you are looking for PV … and FV = 0 once you have repaid the loan! n = 5 yrs * 12 payments per year = 60 payments Since you are “borrowing” money, you are looking for PV … and FV = 0 once you have repaid the loan! n = 5 yrs * 12 payments per year = 60 payments a)What was the original principal amount of the loan? b)What is the balance owed just after the twentieth payment? a)What was the original principal amount of the loan? b)What is the balance owed just after the twentieth payment? Calculating the Original Loan and a Subsequent Balance LO-4

43 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Original Principal = PV of all 60 payments PMT =FV =n = i = c = *12 = 60.08/ PV = 12, Original loan value The required monthly payment on a five-year loan, bearing 8% interest, compounded monthly, is $ a) What was the original principal amount of the loan? b) What is the balance owed just after the twentieth payment? The required monthly payment on a five-year loan, bearing 8% interest, compounded monthly, is $ a) What was the original principal amount of the loan? b) What is the balance owed just after the twentieth payment?

44 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Balance after 20 payments = PV of 40 payments left PMT =FV =n =i = = PV = 8, New loan balance We will leave it to you to do the algebraic solution…! The required monthly payment on a five-year loan, bearing 8% interest, compounded monthly, is $ a) What was the original principal amount of the loan? b) What is the balance owed just after the twentieth payment? The required monthly payment on a five-year loan, bearing 8% interest, compounded monthly, is $ a) What was the original principal amount of the loan? b) What is the balance owed just after the twentieth payment?

45 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© A Deferred Annuity may be viewed as an ordinary annuity that does not begin until a time interval (named the period of deferral) has passed LO-5

46 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Deferred Annuities A Deferred Annuity may be viewed as an ordinary annuity that does not begin until a time interval (named the period of deferral) has passed d = Number of payment intervals in the period of deferral Two-step procedure to find PV: Calculate the present value, PV 1, of the payments at the end of the period of deferral — this is just the PV of an ordinary annuity Calculate the present value, PV 2, of the STEP 1 amount at the beginning of the period of deferral

47 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© … your friend saying the he is repaying a loan at $450 every month for four months. The interest rate he has been charged is 8% compounded monthly. Calculate the amount of the loan, and the amount of interest involved. …this same friend doesn’t begin to repay his loan for another 11 months, at a rate $500 every month for four months. The interest rate is still 8% compounded monthly. Determine the size of the loan. Solve…

48 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© $500 … of the Annuity Present Value of a Deferred Annuity Months 0 PV Step 1 – Determine PV of Annuity 10 months from now Hint: (Use Compound Discount) Step 2 - Discount for 10 months to get today’s Loan Value

49 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© …this same friend doesn’t begin to repay his loan for another 11 months, at a rate $500 every month for four months. The interest rate is still 8% compounded monthly. Determine the size of the loan PV = FV = PV = value 10 months from now loan value today 500

50 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© The payment interval differs from the compounding interval The payment interval differs from the compounding interval e.g. A typical Canadian mortgage has Monthly payments, but the interest is compounded semi-annually Using calculators … LO-6

51 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© For those who are using this type of calculator, the C/Y worksheet will now be used See following REVIEW For those who are using a non-financial calculator, new formulae will be added to find the solution See following

52 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© We can input the number of compoundings per year into the financial calculator. This can be performed by using the symbol To access this symbol use: …and you will see

53 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© The 12 is a default setting This display is referred to as “the worksheet”. … represents the number of P ayments per Y ear … represents the number of C ompoundings per Y ear To access use: Note: You can override these values by entering new ones! …Example Appears automatically Appears automatically

54 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© P/Y = 12.00C/Y = Using C/Y = 2.00 Adding New Formulae Typical Canadian mortgage Interest is compounded semi-annually and payments are each month. Typical Canadian mortgage Interest is compounded semi-annually and payments are each month.

55 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© to calculate the equivalent periodic rate that matches the payment interval C = C = number of interest compoundings per year number of payments per year Use c to determine i 2 Step 2 Use i 2 = (1+i) c - 1 Use this equivalent periodic rate as the value for “ i ” in the appropriate simple annuity formula Step 3 …Example Step 1 D etermine the number of I nterest periods per c ompounding interval Adding New Formulae

56 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Typical Canadian mortgage 6% Interest is compounded semi-annually and payments are each month. Find C and i 2. Typical Canadian mortgage 6% Interest is compounded semi-annually and payments are each month. Find C and i 2. C = C = number of interest compoundings per year number of payments per year Step 1 To determine the number of I nterest periods per c ompounding interval = C Use c to determine i 2 Step 2

57 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Use c to determine i 2 Step 2 i 2 = (1+i) c - 1 i2 =i2 = (1+.06/2) Typical Canadian mortgage 6% Interest is compounded semi-annually and payments are each month. Find C and i 2. Typical Canadian mortgage 6% Interest is compounded semi-annually and payments are each month. Find C and i = i … another example

58 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© % interest is compounded monthly and payments are each week Mortgage Step 1 To determine the number of c ompoundings C = number of interest compoundings per year number of payments per year = C Use c to determine i 2 Step 2

59 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Use c to determine i 2 Step 2 i 2 = (1+i) c - 1 i2 =i2 = (1+.05/12) = i % interest is compounded monthly and payments are each week Mortgage … another example

60 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© You decide to save $50/month for the next three years. If you invest all of these savings in an account which will pay you 7% compounded semi-annually, determine the total in the account after 3 years. Is the following a General Annuity? The payment interval differs from the compounding interval The payment interval differs from the compounding interval Criteria As the Criteria have been met, therefore, we need to determine C

61 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Find i 2 Step 2 i 2 = (1+i) c - 1 i2 =i2 = (1+.07/2) You decide to save $50/month for the next three years. If you invest all of these savings in an account which will pay you 7% compounded semi-annually, determine the total in the account after 3 years. i2 =i2 = Step 1 Find c Use i 2 Step

62 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Formula [ FV= PMT (1+ i) n - 1 i ] You decide to save $50/month for the next three years. If you invest all of these savings in an account which will pay you 7% compounded semi-annually, determine the total in the account after 3 years. PMT =PV =n = i = c = i 2 = *12 = 36.07/2 2/12 = Use i 2 in the appropriate formula Step Solve…

63 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© P/Y = 12C/Y = 12 C/Y = 2 You decide to save $50/month for the next three years. If you invest all of these savings in an account which will pay you 7% compounded semi-annually, determine the total in the account after 3 years FV =

64 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© …your calculator retains at least two more digits than you see displayed! Improving the Accuracy of Calculated Results C = number of interest compoundings per year number of payments per year the value for c can be a repeating decimal SAVE c in memory… when you need the exponent for Simply the c value from memory! The value for i 2 should be saved in memory as soon you calculate it! it later!

65 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Reid David made annual deposits of $1,000 to Fleet Bank, which pays 6% interest compounded annually. After 4 years, Reid makes no more deposits. What will be the balance in the account 10 years after the last deposit?

66 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© … of the Annuity FV 1 Step 2 – Determine FV using compound interest FV 2 Step 1 – Determine FV 1 of Annuity 10 years from now Years $1000 Reid David made annual deposits of $1,000 to Fleet Bank, which pays 6% interest compounded annually. After 4 years, Reid makes no more deposits. What will be the balance in the account 10 years after the last deposit?

67 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Step 1 – Determine FV 1 of Annuity 10 years from now P/Y = 1.00C/Y = 1.00 value at end of 4 years Step 2… FV = Reid David made annual deposits of $1,000 to Fleet Bank, that pays 6% interest compounded annually. After 4 years, Reid makes no more deposits. What will be the balance in the account 10 years after the last deposit? Reid David made annual deposits of $1,000 to Fleet Bank, that pays 6% interest compounded annually. After 4 years, Reid makes no more deposits. What will be the balance in the account 10 years after the last deposit?

68 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Formula solution Step 2 – Determine FV 2 using compound interest FV = FV = value 14 years from now Reid David made annual deposits of $1,000 to Fleet Bank, that pays 6% interest compounded annually. After 4 years, Reid makes no more deposits. What will be the balance in the account 10 years after the last deposit? Reid David made annual deposits of $1,000 to Fleet Bank, that pays 6% interest compounded annually. After 4 years, Reid makes no more deposits. What will be the balance in the account 10 years after the last deposit?

69 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Formula [ FV= PMT (1+ i) n - 1 i ] n =i = c = PMT = Step 1 – Determine FV of Annuity 4 years from now value at end of 4 years Step 2… Reid David made annual deposits of $1,000 to Fleet Bank, that pays 6% interest compounded annually. After 4 years, Reid makes no more deposits. What will be the balance in the account 10 years after the last deposit? Reid David made annual deposits of $1,000 to Fleet Bank, that pays 6% interest compounded annually. After 4 years, Reid makes no more deposits. What will be the balance in the account 10 years after the last deposit?

70 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Step 2 – Determine FV using compound interest Reid David made annual deposits of $1,000 to Fleet Bank, which pays 6% interest compounded annually. After 4 years, Reid makes no more deposits. What will be the balance in the account 10 years after the last deposit? n =i = PV = value 14 years from now FV = PV(1 + i) n Formula

71 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© How much more interest will Reid David accumulate over the 14 years if his account earns 6% compounded daily? P/Y = 10 value at end of 4 years C/Y = 1 C/Y = 365 Step 1 – Determine FV of Annuity 4 years from now 0 FV =

72 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© FV = How much more interest will Reid David accumulate over the 14 years if his account earns 6% compounded daily? value 14 years from now P/Y = 1 P/Y = 365 0FV = Step 2 – Determine FV in 10 years using compound interest

73 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© Interest $7, $7,834.27

74 Ordinary Annuities Ordinary Annuities1010 McGraw-Hill Ryerson© This completes Chapter 10


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