1. O A Ordinary Annuities Present Value Future Chapter 10
McGraw-Hill Ryerson©

2. 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

3. 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

4. - 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

5. … 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

6. 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

7. 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

8. 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

9. 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

10. 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+ $ $
= $

11. Future Value of an Ordinary Simple AnnuityQ
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

12. 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 …

13. Future Value of an Ordinary Simple AnnuityQ
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

14. [ ] = 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

15. Future Value of an Ordinary Simple AnnuityQ
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 =

16. 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...

17. 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…

18. …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 …

19. 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

20. [ ] 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 =

21. 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

22. 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

23. 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

24. 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

25. [ ] 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

26. [ ] = 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

27. 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

28. 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
= $

29. 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…

30. 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

31. [ ] 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

32. Contribution of Each Payment to an Annuity’s Present Value
Diagram

33. 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

34. …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

35. 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. 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

37. 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

38. $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

39. 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…

40. 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

41. 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!

42. 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

43. 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

44. 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…!

45. 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. 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

47. 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…

48. 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

49. 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

50. 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…

51. 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

52. 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

53. 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

54. 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

55. 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

56. . = 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

57. 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

58. 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

59. 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

60. 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

61. 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

62. [ ] 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…

63. 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

64. 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!

65. 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?

66. 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

67. 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…

68. 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

69. 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…

70. 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

71. 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

72. 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

73. Interest $7,992.37 $7,834.27 Summary Daily Annual
$158.l0 more interest

74. This completes Chapter 10