Annuities Ordinary
Annuities
10 10
10 10
McGraw-Hill Ryerson©
1000 1000
1.0 4
1
n = 1
Sum
= FV
of annuity
1 2
3 4
Interval number
1000 1000
1000
1000 1.0
4
2
n = 2
1000 1.0
4
3
n = 3
…the sum of the future values
of all the payments
Assume that there are four4 annual 1000
payments with
interest at 4 Future Value
of an Ordinary Simple Annuity
of an O
rdinary S
imple A
nnuity
LO-2 LO-2
Annuities Ordinary
Annuities
10 10
10 10
McGraw-Hill Ryerson©
= 4
246 .
46
= 1000
+ FV
of annuity 1000
1000 1.0
4
1
n = 1
Sum
= FV
of annuity 1
2 3
4 Interval
number 1000
1000 1000
1000 1.0
4
2
n = 2
1000 1.0
4
3
n = 3 Assume that there are four4 annual
1000 payments
with interest at 4
1000 1.0
4 +
1000 1.0
4
2
+ 1000
1.0 4
3
= 1000
+ 10
40 +
10 81
. 60
+ 1
124 .
86 Future Value
of an Ordinary Simple Annuity
of an O
rdinary S
imple A
nnuity
Annuities Ordinary
Annuities
10 10
10 10
McGraw-Hill Ryerson©
Result Result
500
500 1+
.0 3
12
Sum = FV
of annuity 1
2 3
4 Month
500 500
500
500 1+
.0 3
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+
.0 3
12
2
500 .
00 50
1 .
25 50
2 .
50 50
3 .
76 2,00
7 .
51 Future Value
of an Ordinary Simple Annuity
of an O
rdinary S
imple A
nnuity
Annuities Ordinary
Annuities
10 10
10 10
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
= n =
3 yrs 12
payments per year =
36 payments
of an Ordinary Simple Annuity
of an O
rdinary S
imple A
nnuity
Using the …
Annuities Ordinary
Annuities
10 10
10 10
McGraw-Hill Ryerson©
36 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 .
3
500 Future Value
of an Ordinary Simple Annuity
of an O
rdinary S
imple A
nnuity
12
Using the formula Using the formula
Note Note
Keys direction PY=
120 FV
= 18810.28
Annuities Ordinary
Annuities
10 10
10 10
McGraw-Hill Ryerson©
…
the sum of the future values
of all the payments
of an Ordinary Simple Annuity
of an O
rdinary S
imple A
nnuity
FV
=
PMT 1+
i
n
- 1
[
i
]
Formula Formula
Annuities Ordinary
Annuities
10 10
10 10
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
of an O
rdinary S
imple A
nnuity
0.0025
[
FV =
PMT 1+
i
n
- 1
i
]
1.0025 1.0941
0.0941 37.6206
18810.28
12 .03
500
36
1
1
Annuities Ordinary
Annuities
10 10
10 10
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 =
n = 4
payments PMT
= -500
using Annuities Solving
using Annuities
Annuities Ordinary
Annuities
10 10
10 10
McGraw-Hill Ryerson©
Cash Flows Cash Flows
… payments received e.g. receipts
Treated as: Treated as:
Positives
+
Positives
+
Negatives
-
Negatives
-
..a term that refers to payments that can be either …
..a term that refers to payments that can be either …
… payments made e.g. cheques
Therefore… Therefore…
Annuities Ordinary
Annuities
10 10
10 10
McGraw-Hill Ryerson©
Therefore… Therefore…
…when you are making payments, or even making deposits to
savings,
Really payments to
the bank Really
payments to the bank
these are
cash outflows
,
and therefore the values must be negative
Cash Flow Sign Convention
Using the …
Annuities Ordinary
Annuities
10 10
10 10
McGraw-Hill Ryerson©
You vow to save 500month 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. 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 =
n =
4
payments PMT
-500 Future Value
of an Ordinary Simple Annuity
of an O
rdinary S
imple A
nnuity
4
3
500 12
FV = 2007.51
We already have these from before, so
we don’t have to enter them again
We already have these from before, so
we don’t have to enter them again
Formula solution Formula solution
Annuities Ordinary
Annuities
10 10
10 10
McGraw-Hill Ryerson©
12 .03
500 4
1
1
You vow to save 500month 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. 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 Formula
[
FV =
PMT 1+
i
n
- 1
i
]
PMT =
500
n = 4
i =
. 03
12 =
. 0025
0.0025 1.0025
1.0100 0.0100
4.0150 2007.51
Annuities Ordinary
Annuities
10 10
10 10
McGraw-Hill Ryerson©
Not seeing the total picture Not seeing the total picture
When you use formula or a calculator’s financial functions to
calculate an annuity’s F
uture V
alue,
the amount each payment
contributes to the future value is
NOT apparent
Annuities Ordinary
Annuities
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McGraw-Hill Ryerson©
10 Compounded Annually 10 Compounded Annually
10.00 10.00
Years Years
1 2
3 4
5 14.64
13.31
12.10
11.00
10.00
C
ontribution
61.05 61.05
FV Contributions FV
10.00 10.00
10.00 10.00
10.00 10.00
10.00 10.00
FV FV
Annuities Ordinary
Annuities
10 10
10 10
McGraw-Hill Ryerson©
of an Ordinary Simple Annuity
of an O
rdinary S
imple A
nnuity
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 =
= 7
n = 4
12 =
48
- 75
PV =
FV =
?
Solve…
Total Deposits =
75 48
= 3,600
= 12
Annuities Ordinary
Annuities
10 10
10 10
McGraw-Hill Ryerson©
You decide to save 75month 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 48
7
75 12
Formula solution Formula solution
FV……….. 4,140.69
Interest Earned =
540.69 Deposits…... 3,600.00
PY
= 12
FV
= 4140.69
Annuities Ordinary
Annuities
10 10
10 10
McGraw-Hill Ryerson©
FV 4,140.69
=
Interest Earned 540.69
- Deposits 3,600.00
Formula Formula
FV =
PMT 1+
i
n
- 1
i
0.005833 1.005833
1.32205 0.32205
12 .07
75
48
1
1 55.20924
4140.6927
You decide to save 75month 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
Annuities Ordinary
Annuities
10 10
10 10
McGraw-Hill Ryerson©
…
the sum of the present values
of all the payments
PV
=
PMT 1-1+
i
-n
[
i
]
of an Ordinary Simple Annuity
of an O
rdinary S
imple A
nnuity
Formula Formula
Annuities Ordinary
Annuities
10 10
10 10
McGraw-Hill Ryerson©
1000
Sum
= PV
of annuity
1000 1000
1000
…the sum of the present values
of all the payments
Assume that there are four4 annual 1000
payments with
interest at 4 Present Value
of an Ordinary Simple Annuity
of an O
rdinary S
imple A
nnuity
1000 1.0
4
-1
n = 1
1000 1.0
4
-2
n = 2
1000 1.0
4
-3
n = 3
1000 1.0
4
-4
n = 4
1 2
3 4
Interval Number
Annuities Ordinary
Annuities
10 10
10 10
McGraw-Hill Ryerson©
= 3629.90
PV of annuity
= 1000
1.0 4
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