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**O A Ordinary Annuities Present Value Future Chapter 10**

McGraw-Hill Ryerson©

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**Learning Objectives Define and distinguish between… Calculate the…**

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

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**Learning Objectives Calculate the… LO-4 LO-5 LO-6**

… principal balance owed on a loan immediately after any payment LO-5 … Present Value of and period of deferral of a deferred annuity LO-6 … Future Value and Present Value of ordinary general annuities

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**- A series of equal payments at regular intervals**

Terminology Annuity LO-1 - A series of equal payments at regular intervals Term of the Annuity - the time from the beginning of the first payment period to the end of the last payment period Present Value Future Value 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 the future dollar amount of a series of payments plus interest

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**… is the time between successive payments in an annuity**

Terminology PMT … is the amount of each payment in an annuity n … is the number of payments in the annuity payment interval … is the time between successive payments in an annuity … are ones in which payments are made at the end of each payment interval ordinary annuities Illustration

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**Suppose you obtain a personal loan to be repaid by**

Terminology Illustration Suppose you obtain a personal loan to be repaid by Term 48 months or 4years. payment interval 1 month ordinary annuities 48 equal monthly payments first payment will be due 1 month after you receive the loan, i.e. at the end of the first payment interval Time Diagram

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**Terminology Time Diagram n-1 n 1 2 3 Term of the annuity PMT PMT PMT**

… for an n-payment Ordinary Annuity Payment interval Interval number n-1 n 1 2 3 PMT PMT PMT PMT PMT Term of the annuity

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**Ordinary Annuity Examples Ordinary Simple Annuities**

Ordinary General Annuities The payment interval = the compounding interval The payment interval differs from the compounding interval Monthly payments, and interest is compounded monthly Monthly payments, but interest is compounded semi-annually Examples

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**1 2 3 4 Calculation Sum = FV of annuity Interval number**

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

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**Future Value of an Ordinary Simple Annuity**

Assume that there are four(4) annual $1000 payments with interest at 4% 1 2 3 4 Interval number $1000 $1000 $1000 $1000 n = 1 n = 3 n = 2 $1000 (1.04)1 $1000 (1.04)2 $1000 (1.04)3 Sum = FV of annuity FV of annuity = $1000 + $1000(1.04) + $1000(1.04)2 + $1000(1.04)3 = $1000 + $1040+ $ $ = $

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**Future Value of an Ordinary Simple Annuity**

Q 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. 1 2 3 4 Month Result $500 $500 $500 $500 $ $500(1+.03/12) 501.25 $500(1+.03/12)2 502.50 $500(1+.03/12)3 503.76 Sum = FV of annuity $2,007.51

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**Q Financial Future Value of an Ordinary Simple Annuity**

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 Financial Using the …

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**Future Value of an Ordinary Simple Annuity**

Q 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. ON/OFF FV = P/Y= 2nd P/Y Note 3 I/Y 36 N Keys direction PV 12 ENTER 500 +/- PMT QUIT 2nd CPT FV Using the formula

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**[ ] = PMT i FV (1+ i)n - 1 Future Value of an Ordinary Simple Annuity**

…the sum of the future values of all the payments FV = PMT (1+ i)n - 1 [ i ] Formula

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**Future Value of an Ordinary Simple Annuity**

Q 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. [ FV = PMT (1+ i)n - 1 i ] 0.0025 1.0941 1.0025 0.0941 . = 12 STO .03 + = = 1 y x 36 - 1 = . RCL = X 500 =

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**Q Recall... PV = 0 n = 4 payments PMT = -500 Solving earlier Question**

using Annuities Q 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 Recall...

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**Advanced Business Analyst**

CPT 2nd N % INV LN STO RCL CE/C ENTER CF I/Y X ( 7 4 1 2 5 8 ) PV NPV IRR PMT x 1/ y 9 6 3 +/- ON/OFF FV . - + = QUIT SET DEL INS xP/Y P/Y AMORT BGN CLR TVM K HYP SIN COS TAN RAND X! e DATA STAT BOND ROUND DEPR BRKEVN DATE ICONV PROFIT CLR WORK MEM FORMAT RESET nPr nCr ANS Advanced Business Analyst Keep in Mind Recall... Cash Flows ..a term that refers to payments that can be either … Inflows Outflows … payments received e.g. receipts … payments made e.g. cheques Treated as: Positives + Negatives - Therefore…

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**…when you are making payments, or even making deposits to savings,**

Cash Flow Sign Convention Keep in Mind 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! Financial Using the …

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**Future Value of an Ordinary Simple Annuity**

PV = n = 4 payments PMT -500 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. Q 3 I/Y PV 500 +/- PMT 2nd P/Y 12 QUIT ENTER FV = We already have these from before, so we don’t have to enter them again! 4 N CPT FV Formula solution

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**[ ] Q . = STO + = = y x - = = . RCL X = FV = PMT (1+ i)n - 1 i n = 4**

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. Q Formula [ FV = PMT (1+ i)n - 1 i ] PMT = $500 n = 4 0.0025 4.0150 1.0025 1.0100 0.0100 i = .03/12 = .03 . 12 = STO + 1 = 4 = y x - 1 = = . RCL X 500 =

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**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! Diagram

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**1 2 Annual Payments 3 4 5 FV Contributions Contribution FV $10.00**

10% Compounded Annually FV 1 $10.00 14.64 Annual Payments $10.00 2 $10.00 13.31 3 $10.00 12.10 4 $10.00 11.00 5 10.00 Years $61.05

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**Q Step I/Y P/Y Financial Step Solve… Extract necessary data...**

Future Value of an Ordinary Simple Annuity Q 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 Step Extract necessary data... 4 * 12 = 48 PMT = - $75 I/Y = 7 P/Y = 12 n = PV = 0 FV = ? Total Deposits = $75* 48 = $3,600 Financial Solve… Step

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**Financial Q 2nd P/Y QUIT ENTER I/Y N PV +/- PMT CPT FV**

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 Q FV = P/Y = 2nd P/Y 12 QUIT ENTER 7 I/Y 48 N PV 75 +/- PMT CPT FV FV……….. $4,140.69 Deposits…... 3,600.00 Interest Earned = $ Formula solution

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**[ ] Q . = STO + = = y x = - = . RCL X = FV = PMT (1+ i)n - 1 i**

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 Q . = .07 12 STO + = = 1 y x 48 = - 1 = . RCL X 75 = FV $4,140.69 - Deposits 3,600.00 = Interest Earned $540.69

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**[ ] = PMT i Illustration 1-(1+ i)-n PV**

PresentValue of an Ordinary Simple Annuity …the sum of the present values of all the payments PV = PMT 1-(1+ i)-n [ i ] Formula Illustration

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**Calculation 1 2 3 4 Present Value of an Ordinary Simple Annuity**

Assume that there are four(4) annual $1000 payments with interest at 4% 1 2 3 4 Interval Number $1000 $1000 $1000 $1000 n = 3 n = 1 n = 4 n = 2 $1000 (1.04)-1 $1000 (1.04)-2 $1000 (1.04)-3 $1000 (1.04)-4 Sum = PV of annuity …the sum of the present values of all the payments Calculation

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**Present Value of an Ordinary Simple Annuity**

Assume that there are four(4) annual $1000 payments with interest at 4% 1 2 3 4 Interval Number $1000 $1000 $1000 $1000 n = 2 n = 3 n = 4 n = 1 $1000 (1.04)-1 $1000 (1.04)-2 $1000 (1.04)-3 $1000 (1.04)-4 PV of annuity Sum = PV of annuity = $1000(1.04)-1 + $1000(1.04)-2 + $1000(1.04)-3 + $1000 (1.04)-4 = $ $ $ $854.80 = $

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**Q Note Financial Solve… 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. Note …Since you are making payments, not receiving them, PMT = -450 … n = 9 payments … Repaid 9 payments at $450 = $4,050 … Interest - use 12, not .12 when using financial calculator … At the end of the loan, you don’t owe any money, so FV = 0 Financial Solve…

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**Financial Q 2nd P/Y QUIT ENTER I/Y N FV +/- PMT CPT PV**

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. Q 2nd P/Y 12 QUIT ENTER PV = 3,918.24 8 I/Y 9 N FV 450 +/- PMT CPT PV Amount Borrowed (PV) $ 3,918.24 Repaid.…………………. 4,050.00 $ Interest Paid = Formula solution

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**[ ] Q . = STO + = = y x +/- - = +/- . RCL X = i PV = PMT 1-(1+ i)-n**

Formula i PV = PMT 1-(1+ i)-n [ ] 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. Q 3,918.24 . = .08 12 STO + = = 1 y x 9 +/- - 1 = +/- . RCL X 450 = Repaid $4,050.00 - Borrowed $3,918.24 = Interest Charged $131.76

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**Contribution of Each Payment to an Annuity’s Present Value**

Diagram

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**1 2 Annual Payments 3 4 5 PV Contributions Contribution PV $10.00**

9.09 Annual Payments $10.00 2 8.20 $10.00 3 7.51 $10.00 4 $10.00 6.83 5 $10.00 6.21 Years $37.91

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**…of a cash flow stream that includes an annuity**

Ordinary Annuities 10 LO-3 Fair Market Value …of a cash flow stream that includes an annuity

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**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

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**On what information should we focus?**

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 Concept 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.) Therefore... Back to Offer Comparison

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**You have received two offers on a building lot that you want to sell**

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. Summary of Offers Ms. Armstrong Mr. Belcher $25,000 down $20,000 down plus a $100,000 lump sum payment five years from now plus $5000 every quarter for five years Focal Date: Today Preparing Time Lines

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**$25,000 down plus a $100,000 lump sum payment five years from now**

Time Lines A $25,000 down plus a $100,000 lump sum payment five years from now B $20,000 down plus $5,000 every quarter for five years Years 1 2 3 4 5 $25,000 Ms. Armstrong $100,000 Mr.Belcher $20,000 $5000 every quarter $20,000 $20,000 $20,000 $20,000 $20,000 Financial

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**today’s value of Ms. A’s total offer today’s value of lump sum**

Financial Step 1–Determine today’s value of Ms. Armstrong’s 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. Q today’s value of Ms. A’s total offer today’s value of lump sum PV= 103,352.62 100,000 2nd P/Y 1 QUIT ENTER FV 5 5 N I/Y PMT CPT PV + 25,000 Step 2…

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**Step 2 – Determine today’s value of Mr. Belcher’s offer.**

Financial Step 2 – Determine today’s value of Mr. Belcher’s 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. Q today’s value of Mr. B’s total offer today’s value of lump sum P/Y = C/Y = 99,376.93 PV = 79,376.93 2nd P/Y 5 I/Y FV 4 4500 PMT ENTER 20 N CPT PV 1 + 20000 ENTER QUIT 2nd Comparison

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**Comparison $103,352.62 99,376.93 $ 3,975.69 Total Value of each offer**

Ms. Armstrong $103,352.62 99,376.93 Mr.Belcher $ 3,975.69 Difference in Offers Better off accepting Ms. Armstrong’s offer!

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**Calculating the Original Loan and a Subsequent Balance**

The required monthly payment on a five-year loan, bearing 8% interest, compounded monthly, is $ What was the original principal amount of the loan? What is the balance owed just after the twentieth payment? 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

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**Q Financial 2nd P/Y QUIT ENTER FV I/Y PMT N CPT PV c =**

Original Principal = PV of all 60 payments PMT = FV = n = i = c = 249.10 5*12 = 60 .08/12 1 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? Q Financial Original loan value PV = 12,285.22 2nd P/Y 12 QUIT ENTER 8 FV I/Y 249.10 PMT 60 N CPT PV

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**Balance after 20 payments = PV of 40 payments left**

PMT = 249.10 FV = n = = 40 i = .08 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? Q Financial New loan balance PV = 8,720.75 40 N CPT PV We will leave it to you to do the algebraic solution…!

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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

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**d = Number of payment intervals in the period of deferral**

Deferred Annuities d = Number of payment intervals in the period of deferral 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 Two-step procedure to find PV: Calculate the present value, PV1, of the payments at the end of the period of deferral — this is just the PV of an ordinary annuity Calculate the present value, PV2, of the STEP 1 amount at the beginning of the period of deferral

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**Remember What if... Financial Solve…**

… 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. What if... …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. Financial Solve…

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**Calculation 10 11 12 13 14 PV Present Value of a Deferred Annuity**

Step 1 – Determine PV of Annuity 10 months from now 10 11 12 13 14 Months $500 $500 $500 $500 PV …of the Annuity Step 2 - Discount for 10 months to get today’s Loan Value Hint: (Use Compound Discount) Calculation

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**Financial FV I/Y 2nd P/Y QUIT ENTER PMT N CPT PV FV PMT N CPT PV**

…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. loan value today value 10 months from now PV = PV = FV = 8 FV I/Y 2nd P/Y 12 QUIT ENTER 500 4 PMT N CPT PV FV PMT 10 N CPT PV

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**the compounding interval**

General Annuities The payment interval differs from the compounding interval LO-6 e.g. A typical Canadian mortgage has Monthly payments, but the interest is compounded semi-annually Using calculators…

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**General Annuities Financial**

See following REVIEW For those who are using this type of calculator, the C/Y worksheet will now be used Financial See following For those who are using a non-financial calculator, new formulae will be added to find the solution

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**Advanced Business Analyst**

General Annuities CPT 2nd N % INV LN STO RCL CE/C ENTER CF I/Y X ( 7 4 1 2 5 8 ) PV NPV IRR PMT x 1/ y 9 6 3 +/- ON/OFF FV . - + = QUIT SET DEL INS xP/Y P/Y AMORT BGN CLR TVM K HYP SIN COS TAN RAND X! e DATA STAT BOND ROUND DEPR BRKEVN DATE ICONV PROFIT CLR WORK MEM FORMAT RESET nPr nCr ANS Advanced Business Analyst We can input the number of compoundings per year into the financial calculator This can be performed by using the symbol Review P/Y To access this symbol use: 2nd I/Y …and you will see

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**The 12 is a default setting**

P/Y= 12 This display is referred to as “the worksheet”. … represents the number of Payments per Year P/Y … represents the number of Compoundings per Year C/Y To access use: C/Y C/Y= 12 Appears automatically Note: You can override these values by entering new ones! …Example

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**General Annuities ON/OFF 2nd P/Y ENTER Financial ENTER 2nd QUIT Using**

Typical Canadian mortgage Interest is compounded semi-annually and payments are each month. P/Y = C/Y = C/Y = P/Y Financial Using 12 ENTER 2 ENTER 2nd QUIT Adding New Formulae

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**C = General Annuities Adding New Formulae**

Step 1 Determine the number of Interest periods per compounding interval C = number of interest compoundings per year number of payments per year Use c to determine i2 Step 2 to calculate the equivalent periodic rate that matches the payment interval Use i2 = (1+i)c - 1 Use this equivalent periodic rate as the value for “i” in the appropriate simple annuity formula Step 3 …Example

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**. = STO C = 2 12 Typical Canadian mortgage 0.166666 Step 1**

To determine the number of Interest periods per compounding interval C = number of interest compoundings per year number of payments per year Typical Canadian mortgage 6% Interest is compounded semi-annually and payments are each month. Find C and i2. = C 2 . 12 = STO Use c to determine i2 Step 2

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**Typical Canadian mortgage**

Use c to determine i2 Step 2 i2 = (1+i)c - 1 Typical Canadian mortgage 6% Interest is compounded semi-annually and payments are each month. Find C and i2. i2 = (1+ .06/2) = i2 1.0049 0.0049 = 1.03 y x RCL - = 1 …another example

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**General Annuities . = STO 12 52 Mortgage**

Step 1 To determine the number of compoundings C = number of interest compoundings per year number of payments per year 5% interest is compounded monthly and payments are each week Mortgage = C 12 . 52 = STO Use c to determine i2 Step 2

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**5% interest is compounded monthly and payments are each week**

Use c to determine i2 Step 2 i2 = (1+i)c - 1 5% interest is compounded monthly and payments are each week Mortgage i2 = (1+ .05/12) = i2 0.05 . 12 = + 1 = = y x RCL - = 1 …another example

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**Q Criteria Is the following a General Annuity?**

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. Criteria The payment interval differs from the compounding interval As the Criteria have been met, therefore, we need to determine C

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**Q . = STO i2 = (1+i)c - 1 i2 = i2 = = y x RCL - = STO 1.00575 0.00575**

Step 1 Find c 0.1666 Q 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 years. 2 . = 12 STO i2 = (1+i)c - 1 Find i2 Step 2 i2 = (1+ .07/2) i2 = = 1.035 y x RCL - = 1 STO Use i2 Step 3

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**[ ] Q + y x - . RCL X Financial c = Solve… FV = PMT (1+ i)n - 1 i**

Use i2 in the appropriate formula Step 3 Formula [ FV = PMT (1+ i)n - 1 i ] Q 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 years. PMT = 50 PV = n = 3*12 = 36 c = i = .07/2 2/12 = i2 = + 1 y x 36 - 1 . RCL X 50 Financial Solve…

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**Financial Q ON/OFF 2nd P/Y ENTER PMT N PV ENTER CPT FV 2nd QUIT**

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 years. ON/OFF 2nd C/Y = FV = P/Y = C/Y = P/Y 12 ENTER 50 36 PMT N 2 7 PV ENTER CPT FV 2nd QUIT

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**1. Tip 2. x y RCL 3. RCL when you need the exponent for**

number of interest compoundings per year number of payments per year 1. Improving the Accuracy of Calculated Results Tip the value for c can be a repeating decimal SAVE c in memory… …your calculator retains at least two more digits than you see displayed! 2. when you need the exponent for y x the c value from memory! RCL Simply The value for i2 should be saved in memory as soon you calculate it! 3. RCL it later!

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Reid David made annual deposits of $1, to Fleet Bank, which pays % interest compounded annually After 4 years, Reid makes no more deposits. What will be the balance in the account years after the last deposit?

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**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 years after the last deposit? Q Step 1 – Determine FV1 of Annuity 10 years from now 1 2 3 4 14 Years $1000 $1000 $1000 $1000 FV1 …of the Annuity Step 2 – Determine FV using compound interest FV2 Calculation

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**Step 1 – Determine FV1 of Annuity 10 years from now**

Financial Step 1 – Determine FV1 of Annuity 10 years from now Reid David made annual deposits of $1,000 to Fleet Bank, that pays % interest compounded annually After 4 years, Reid makes no more deposits. What will be the balance in the account years after the last deposit? Q value at end of years 2nd P/Y P/Y = C/Y = FV = 1 ENTER 6 I/Y PV 1000 4 PMT N 1 ENTER CPT FV QUIT 2nd Step 2…

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**Step 2 – Determine FV2 using compound interest**

Financial Step 2 – Determine FV2 using compound interest Reid David made annual deposits of $1,000 to Fleet Bank, that pays % interest compounded annually After 4 years, Reid makes no more deposits. What will be the balance in the account years after the last deposit? Q FV = value 14 years from now FV = PV PMT 10 N CPT FV Formula solution

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**Step 1 – Determine FV of Annuity 4 years from now**

Formula [ FV = PMT (1+ i)n - 1 i ] Reid David made annual deposits of $1,000 to Fleet Bank, that pays % interest compounded annually After 4 years, Reid makes no more deposits. What will be the balance in the account years after the last deposit? Q PMT = 1000 n = 4 i = 0.06 c = 1 value at end of 4 years 4 1.06 y x - 1 . 0.06 X 1000 STO Step 2…

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**Step 2 – Determine FV using compound interest**

FV = PV(1 + i)n Formula Q Reid David made annual deposits of $1,000 to Fleet Bank, which pays % interest compounded annually After 4 years, Reid makes no more deposits. What will be the balance in the account years after the last deposit? n = i = 0.06 PV = 10 value 14 years from now 1.06 y x 10 X RCL

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**Step 1 – Determine FV of Annuity 4 years from now**

Financial Step 1 – Determine FV of Annuity 4 years from now ON/OFF Q 2nd value at end of 4 years How much more interest will Reid David accumulate over the 14 years if his account earns 6% compounded daily? P/Y = FV = C/Y = C/Y = P/Y 1 ENTER 1000 4 PMT N 365 6 PV ENTER 2nd CPT FV QUIT

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**Step 2 – Determine FV in 10 years using compound interest**

Financial Step 2 – Determine FV in 10 years using compound interest Q 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 = FV = P/Y = FV = PV 2nd P/Y 3650 PMT N 365 ENTER CPT FV 2nd QUIT

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**Interest $7,992.37 $7,834.27 Summary Daily Annual**

$158.l0 more interest

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**This completes Chapter 10**

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