# Present Value Calculator

Document Sample

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Mathematics
of Finance            With a Financial Calculator

Presentation
2
Compound Value
Parameters:
Interest rate (i)
Amount that is invested, present value (PV)
Time money remains invested (n)
Future value of the investment in n years (FVn)
Periodic equal payment (or deposit) (PMT)
3
Compound Value
Future Value of a Lump Sum (one time payment):
Value at some time in the future of an investment
Interest compounds: earn interest on interest in later
years.
Future value in one year is present value plus the
interest that is earned over the year.
4
Compound Value
Future Value of a Lump Sum (one time payment):
In General

FVn = PV(1+ i)n
5
Compound Value
Present Value of a Lump Sum (one time payment):
Value today of an amount to be received or paid in
the future.
FVn
PV =
(1 + i)n

Example: Expect to receive \$100 in eight years. If can
invest at 10%, what is it worth today?
6
Compound Value
Present Value of a Lump Sum (one time payment):
Value today of an amount to be received or paid in
the future.
FV8
PV =
(1 + i)8

Example: Expect to receive \$100 in EIGHT years. If can
invest at 10%, what is it worth today?
0    1    2   3    4    5    6    7     8

?                                     \$100
7
Compound Value
Present Value of a Lump Sum (one time payment):
Value today of an amount to be received or paid in
the future.
FV8
PV =
(1 + i)8

Example: Expect to receive \$100 in EIGHT years. If can
invest at 10%, what is it worth today?
0    1    2   3    4    5    6    7     8

?                                     \$100
8
Financial Calculator
Setting Display
Should show at least 2
decimal places on dollar                 0.00
amounts and 4 decimal
places on percentages                                  P/YR
N   I/YR PV PMT FV

CLEAR ALL
INPUT

7      8           9     
4      5           6     x

1      2           3     –
BEG/END              DISP
0      .           =     +
HP10B Calculator
9
Financial Calculator
Setting Display
Should show at least 2
decimal places on dollar                 0.00
amounts and 4 decimal
places on percentages                                  P/YR
N   I/YR PV PMT FV

CLEAR ALL
INPUT

7      8           9     
4      5           6     x
1
1      2           3     –
BEG/END              DISP
0      .           =     +
HP10B Calculator
10
Financial Calculator
Setting Display
Should show at least 2
decimal places on dollar                 0.00
amounts and 4 decimal
places on percentages                                  P/YR
N   I/YR PV PMT FV

CLEAR ALL
INPUT

7      8           9     
4      5           6     x
1
1      2           3     –
2        BEG/END              DISP
0      .           =     +
HP10B Calculator
11
Financial Calculator
Setting Display
Should show at least 2
decimal places on dollar                 0.0000
amounts and 4 decimal
places on percentages                                  P/YR
N   I/YR PV PMT FV

CLEAR ALL
INPUT

3           7      8           9     
4      5           6     x
1
1      2           3     –
2        BEG/END              DISP
0      .           =     +
HP10B Calculator
12
Financial Calculator
Clearing Memory
Financial calculators contain
a number of memory                      0.0000
registers. These registers
should be cleared to                                  P/YR
prevent carry-over errors.          N   I/YR PV PMT FV

CLEAR ALL
INPUT

7      8           9     
4      5           6     x

1      2           3     –
BEG/END              DISP
0      .           =     +
HP10B Calculator
13
Financial Calculator
Clearing Memory
Financial calculators contain
a number of memory                      0.0000
registers. These registers
should be cleared to                                  P/YR
prevent carry-over errors.          N   I/YR PV PMT FV

CLEAR ALL
INPUT

7      8           9     

1              4      5           6     x

1      2           3     –
BEG/END              DISP
0      .           =     +
HP10B Calculator
14
Financial Calculator
Clearing Memory
Financial calculators contain
a number of memory                      0.0000
registers. These registers
should be cleared to                                  P/YR
prevent carry-over errors.          N   I/YR PV PMT FV

2
CLEAR ALL
INPUT

7      8           9     

1              4      5           6     x

1      2           3     –
BEG/END              DISP
0      .           =     +
HP10B Calculator
15
Financial Calculator
Setting Compounding Frequency
Compounding should be set
to annual, i.e. P/YR=1, not            0.0000
the factory setting of 12.
P/YR
N   I/YR PV PMT FV

CLEAR ALL
INPUT

7      8           9     
4      5           6     x

1      2           3     –
BEG/END              DISP
0      .           =     +
HP10B Calculator
16
Financial Calculator
Setting Compounding Frequency
Compounding should be set
to annual, i.e. P/YR=1, not            1.0000
the factory setting of 12.
P/YR
N   I/YR PV PMT FV

CLEAR ALL
INPUT

7      8           9     
1
4      5           6     x

1      2           3     –
BEG/END              DISP
0      .           =     +
HP10B Calculator
17
Financial Calculator
Setting Compounding Frequency
Compounding should be set
to annual, i.e. P/YR=1, not            1.0000
the factory setting of 12.
P/YR
N   I/YR PV PMT FV

CLEAR ALL
INPUT

7      8           9     
1
4      5           6     x
2
1      2           3     –
BEG/END              DISP
0      .           =     +
HP10B Calculator
18
Financial Calculator
Setting Compounding Frequency
Compounding should be set
to annual, i.e. P/YR=1, not            1.0000
the factory setting of 12.
P/YR
N   I/YR PV PMT FV

3       CLEAR ALL
INPUT

7      8           9     
1
4      5           6     x
2
1      2           3     –
BEG/END              DISP
0      .           =     +
HP10B Calculator
19
Financial Calculator
Setting Compounding Frequency
Compounding should be set
to annual, i.e. P/YR=1, not             1 P/Yr
the factory setting of 12.
To check setting CLEAR the                            P/YR

calculator (holding down the        N   I/YR PV PMT FV
CLEAR ALL key)
CLEAR ALL
INPUT
2
7      8           9     
1               4      5           6     x

1      2           3     –
BEG/END              DISP
0      .           =     +
HP10B Calculator
20
Financial Calculator Solution
Present Value of a Lump Sum (one time payment):
Previous Example:
Example: Expect to receive \$100 in EIGHT years. If can
invest at 10%, what is it worth today?
0    1    2   3       4   5   6   7    8     9   10

?                                     \$100

Using Formula:
100
PV = (1+.1)8 = 46.65
21
Financial Calculator Solution
Present Value of a Lump Sum (one time payment):
Previous Example:
Example: Expect to receive \$100 in EIGHT years. If can
invest at 10%, what is it worth today?
0    1    2   3    4    5    6   7     8      9   10

?                                     \$100

8.0000

N   I/YR PV PMT FV

8
22
Financial Calculator Solution
Present Value of a Lump Sum (one time payment):
Previous Example:
Example: Expect to receive \$100 in EIGHT years. If can
invest at 10%, what is it worth today?
0    1    2      3    4    5       6   7      8     9   10

?                                           \$100

10.000

N   I/YR PV PMT FV
Enter the Interest
Rate as a WHOLE #        8 10
23
Financial Calculator Solution
Present Value of a Lump Sum (one time payment):
Previous Example:
Example: Expect to receive \$100 in EIGHT years. If can
invest at 10%, what is it worth today?
0    1    2   3    4    5    6   7      8    9   10

?                                     \$100

100.0000

N   I/YR PV PMT FV

8 10            100
24
Financial Calculator Solution
Present Value of a Lump Sum (one time payment):
Previous Example:
Example: Expect to receive \$100 in EIGHT years. If can
invest at 10%, what is it worth today?
0    1    2   3    4    5    6   7      8       9   10

?                                     \$100

- 46.65

N   I/YR PV PMT FV

8 10       ?       100
25
Compound Value
Present Value of a Lump Sum (one time payment):
Previous Example:
Example: Expect to receive \$100 in EIGHT years. If can
invest at 10%, what is it worth today?
0    1     2    3     4    5     6   7      8      9   10

?                                         \$100

Can change any or all parameters
without reentering others

N   I/YR PV PMT FV

8    10           100
26
Compound Value
Present Value of a Lump Sum (one time payment):
Previous Example:
Example: Expect to receive \$100 in EIGHT years. If can
invest at 10%, what is it worth today?
0    1     2    3     4    5     6   7     8       9   10

?                                         \$100

Can change any or all parameters
without reentering others

Change Interest rate to          N   I/YR PV PMT FV
5%                               8    10           100
5
27
Compound Value
Present Value of a Lump Sum (one time payment):
Previous Example:
Example: Expect to receive \$100 in EIGHT years. If can
invest at 10%, what is it worth today?
0    1     2    3     4    5     6   7      8          9   10

?                                         \$100

Can change any or all parameters
without reentering others

Change Interest rate to          N   I/YR PV PMT FV
5%                               8    10       ?       100
5
28
Compound Value
Present Value of a Lump Sum (one time payment):
Previous Example:
Example: Expect to receive \$100 in EIGHT years. If can
invest at 10%, what is it worth today?
0    1     2    3    4     5    6   7     8      9   10

?                                        \$100

Can check the number entered in
each memory location using the
recall (RCL) key.
N   I/YR PV PMT FV

RCL
29
Compound Value
Present Value of a Lump Sum (one time payment):
Previous Example:
Example: Expect to receive \$100 in EIGHT years. If can
invest at 10%, what is it worth today?
0    1     2    3    4     5    6   7     8      9   10

?                                        \$100

Can check the number entered in
each memory location using the
recall (RCL) key.
N   I/YR PV PMT FV

Check setting for years:            RCL
30
Compound Value
Solve for other parameters (I/YR)
Given any three of the following: PV, FV, i and n, the
fourth can be computed.
31
Compound Value
Solve for other parameters (I/YR)
Given any three of the following: PV, FV, i and n, the
fourth can be computed.
Example: A \$200 investment has grown to \$230 over two years.
What is the ANNUAL return on this investment?
0                  1                  2

\$200                                  \$230
32
Compound Value
Solve for other parameters (I/YR)
Given any three of the following: PV, FV, i and n, the
fourth can be computed.
Example: A \$200 investment has grown to \$230 over two years.
What is the ANNUAL return on this investment?
0                  1                  2

\$200                                  \$230
33
Compound Value
Solve for other parameters (I/YR)
Given any three of the following: PV, FV, i and n, the
fourth can be computed.
Example: A \$200 investment has grown to \$230 over two years.
What is the ANNUAL return on this investment?
0                    1                2

\$200                                  \$230

0.00
or FVn = PV(1+ i)n
N   I/YR PV PMT FV
34
Compound Value
Solve for other parameters (I/YR)
Given any three of the following: PV, FV, i and n, the
fourth can be computed.
Example: A \$200 investment has grown to \$230 over two years.
What is the ANNUAL return on this investment?
0                    1                2

\$200                                  \$230

2.00
or FVn = PV(1+ i)n
N   I/YR PV PMT FV

2
35
Compound Value
Solve for other parameters (I/YR)
Given any three of the following: PV, FV, i and n, the
fourth can be computed.
Example: A \$200 investment has grown to \$230 over two years.
What is the ANNUAL return on this investment?
0                   1                   2

\$200                                   \$230

2.00            When Entering inflows
n and outflows of cash,
or FVn = PV(1+ i) enter as follows:
(-) = cash outflow
N I/YR PV PMT FV
(+) = cash inflow
2
36
Compound Value
Solve for other parameters (I/YR)
Given any three of the following: PV, FV, i and n, the
fourth can be computed.
Example: A \$200 investment has grown to \$230 over two years.
What is the ANNUAL return on this investment?
0                  1                    2

\$200                                   \$230

– 200.00        When Entering inflows
n and outflows of cash,
or FVn = PV(1+ i) enter as follows:
(-) = cash outflow
N I/YR PV PMT FV
(+) = cash inflow
2       -200
37
Compound Value
Solve for other parameters (I/YR)
Given any three of the following: PV, FV, i and n, the
fourth can be computed.
Example: A \$200 investment has grown to \$230 over two years.
What is the ANNUAL return on this investment?
0                      1              2

\$200                                  \$230

230.00
or FVn = PV(1+ i)n
N   I/YR PV PMT FV

2       -200     230
38
Compound Value
Solve for other parameters (I/YR)
Given any three of the following: PV, FV, i and n, the
fourth can be computed.
Example: A \$200 investment has grown to \$230 over two years.
What is the ANNUAL return on this investment?
0                     1               2

\$200                                  \$230

7.24
or FVn = PV(1+ i)n
N   I/YR PV PMT FV

2    ?     -200   230
39
Compound Value
Solve for other parameters (N)
Given any three of the following: PV, FV, i and n, the
forth can be computed.
Example: How long will it take for a \$300 investment to
grow to \$500 if 6% annual interest is earned?
40
Compound Value
Solve for other parameters (N)
Given any three of the following: PV, FV, i and n, the
forth can be computed.
Example: How long will it take for a \$300 investment to
grow to \$500 if 6% annual interest is earned?
0                    1                   N

\$300                                     \$500
41
Compound Value
Solve for other parameters (N)
Given any three of the following: PV, FV, i and n, the
forth can be computed.
Example: How long will it take for a \$300 investment to
grow to \$500 if 6% annual interest is earned?
0                    1                   N

\$300                                     \$500
42
Compound Value
Solve for other parameters (N)
Given any three of the following: PV, FV, i and n, the
forth can be computed.
Example: How long will it take for a \$300 investment to
grow to \$500 if 6% annual interest is earned?
0                    1                   N

\$300                                     \$500

– 300.00

N   I/YR PV PMT FV

-300
43
Compound Value
Solve for other parameters (N)
Given any three of the following: PV, FV, i and n, the
forth can be computed.
Example: How long will it take for a \$300 investment to
grow to \$500 if 6% annual interest is earned?
0                       1                N

\$300                                     \$500

500.00

N   I/YR PV PMT FV

-300     500
44
Compound Value
Solve for other parameters (N)
Given any three of the following: PV, FV, i and n, the
forth can be computed.
Example: How long will it take for a \$300 investment to
grow to \$500 if 6% annual interest is earned?
0                      1                 N

\$300                                     \$500

6.00

N   I/YR PV PMT FV

6     -300   500
45
Compound Value
Solve for other parameters (N)
Given any three of the following: PV, FV, i and n, the
forth can be computed.
Example: How long will it take for a \$300 investment to
grow to \$500 if 6% annual interest is earned?
0                      1                 N

\$300                                     \$500

8.77

N   I/YR PV PMT FV

?    6     -300   500
46
Non-Annual Compounding
All equations and calculator solutions thus far have
assumed compounding occurs ONCE a year.
47
Non-Annual Compounding
All equations and calculator solutions thus far have
assumed compounding occurs ONCE a year.
Example: Deposit \$1,000 at 10% nominal annual interest rate.
How much will you have at end of 1 year?
ANNUAL COMPOUNDING
0                                      1

\$1,000
\$1,000(1.1)
\$1,100
SEMI-ANNUAL COMPOUNDING
0                6 months              1

\$1,000
48
Non-Annual Compounding
All equations and calculator solutions thus far have
assumed compounding occurs ONCE a year.
Example: Deposit \$1,000 at 10% nominal annual interest rate.
How much will you have at end of 1 year?
ANNUAL COMPOUNDING
0                                      1

\$1,000
\$1,000(1.1)
\$1,100
Earn 10%/2=5%
SEMI-ANNUAL COMPOUNDING                          each compounding
period
0                     6 months         1

\$1,000
\$1,000(1.05)
\$1,050
49
Non-Annual Compounding
All equations and calculator solutions thus far have
assumed compounding occurs ONCE a year.
Example: Deposit \$1,000 at 10% nominal annual interest rate.
How much will you have at end of 1 year?
ANNUAL COMPOUNDING
0                                                  1

\$1,000
\$1,000(1.1)
\$1,100
Earn 10%/2=5%
SEMI-ANNUAL COMPOUNDING                                      each compounding
period
0                     6 months                     1

\$1,000
\$1,000(1.05)
\$1,050
\$1,050(1.05)
\$1,102.50
50
Non-Annual Compounding
All equations and calculator solutions thus far have
assumed compounding occurs ONCE a year.
When compounding more than once a year, must
i mn     m = # of compounding
FVn =   PV(1+m)           periods in a year
51
Non-Annual Compounding
All equations and calculator solutions thus far have
assumed compounding occurs ONCE a year.
When compounding more than once a year, must
i mn        m = # of compounding
FVn =   PV(1+m)              periods in a year

Example: Deposit \$1,800 at 8% nominal annual interest rate,
compounded quarterly. How much will you have at
end of 3 years?
52
Financial Calculator Solutions
Setting Compounding Frequency
Calculator makes
compounding periods based
on the setting of P/YR           xP/YR              P/YR

For Quarterly compounding         N      I/YR PV PMT FV
set P/YR = 4
3       CLEAR ALL
INPUT

7     8           9     
1
4     5           6     x
2
1     2           3     –
BEG/END              DISP
0     .           =     +
HP10B Calculator
53
Financial Calculator Solutions
Setting Compounding Frequency
Calculator makes
compounding periods based
on the setting of P/YR           xP/YR              P/YR

For Quarterly compounding         N      I/YR PV PMT FV
set P/YR = 4
I/YR/YR is automatically         CLEAR ALL

setting.                                  7     8           9     
4     5           6     x

1     2           3     –
BEG/END              DISP
0     .           =     +
HP10B Calculator
54
Financial Calculator Solutions
Setting Compounding Frequency
Calculator makes
compounding periods based
on the setting of P/YR            xP/YR              P/YR

For Quarterly compounding          N      I/YR PV PMT FV
set P/YR = 4
I/YR/YR is automatically          CLEAR ALL

adjusted by the P/YR      3        INPUT
setting.                                   7     8           9     
To adjust N by P/YR enter                  4     5           6     x
the number of years on the
xP/YR key.                                 1     2           3     –
2            BEG/END              DISP
1
0     .           =     +
HP10B Calculator
55
Non-Annual Compounding
All equations and calculator solutions thus far have
assumed compounding occurs ONCE a year.
When compounding more than once a year, must
i mn      m = # of compounding
FVn =      PV(1+m)            periods in a year

Example: Deposit \$1,800 at 8% nominal annual interest rate,
compounded quarterly. How much will you have at
end of 3 years?                               P/Yr = 4
12.00

Enter Years using Shift [xP/YR]
xP/YR           P/YR
combination
N      I/YR PV PMT FV
3
56
Non-Annual Compounding
All equations and calculator solutions thus far have
assumed compounding occurs ONCE a year.
When compounding more than once a year, must
i mn        m = # of compounding
FVn =   PV(1+m)              periods in a year

Example: Deposit \$1,800 at 8% nominal annual interest rate,
compounded quarterly. How much will you have at
end of 3 years?                               P/Yr = 4
8.00

xP/YR          P/YR
N      I/YR PV PMT FV
3       8
57
Non-Annual Compounding
All equations and calculator solutions thus far have
assumed compounding occurs ONCE a year.
When compounding more than once a year, must
i mn        m = # of compounding
FVn =   PV(1+m)              periods in a year

Example: Deposit \$1,800 at 8% nominal annual interest rate,
compounded quarterly. How much will you have at
end of 3 years?                               P/Yr = 4
– 1800.00

xP/YR                P/YR
N      I/YR PV PMT FV
3       8   -1800
58
Non-Annual Compounding
All equations and calculator solutions thus far have
assumed compounding occurs ONCE a year.
When compounding more than once a year, must
i mn        m = # of compounding
FVn =   PV(1+m)              periods in a year

Example: Deposit \$1,800 at 8% nominal annual interest rate,
compounded quarterly. How much will you have at
end of 3 years?                               P/Yr = 4
2,282.84

xP/YR                P/YR
N      I/YR PV PMT FV
3       8   -1800          ?
59
Financial Calculator Solutions
Automatic
Alternative Settings
P/Yr = 4
Calculator make                   2,282.84
automatically based on    xP/YR                P/YR
P/YR setting.              N      I/YR PV PMT FV
3       8   -1800           ?
60
Financial Calculator Solutions
Automatic
Alternative Settings
P/Yr = 4
Calculator make                    2,282.84
automatically based on       xP/YR          P/YR
P/YR setting.                  N I/YR PV PMT       FV
You can keep P/YR=1 and        3 8 -1800            ?
and I/YR manually.          Manual
Advantage: should never                            P/Yr = 1
need to change P/YR,               2,282.84
therefore fewer errors on
later problems.                             P/YR
If change P/YR, always         N I/YR PV PMT       FV
change back to 1 P/YR after    12 2 -1800           ?
doing problem.
61
Future Value of an Annuity
Annuity- string of deposits with constant value and
fixed interval.
0             1              2              3

\$0            \$100          \$100          \$100

Compute FV3
How much would this account have in it at the end of 3
years if interest were earned at a rate of 8% annually?
62
Future Value of an Annuity
Annuity- string of deposits with constant value and
fixed interval.
0             1                  2          3

\$0            \$100           \$100         \$100
Compute FV3
How much would this account have in it at the end of 3
years if interest were earned at a rate of 8% annually?

3.00

N   I/YR PV PMT FV
3
63
Future Value of an Annuity
Annuity- string of deposits with constant value and
fixed interval.
0             1                  2          3

\$0            \$100           \$100         \$100
Compute FV3
How much would this account have in it at the end of 3
years if interest were earned at a rate of 8% annually?

8.00

N   I/YR PV PMT FV
3    8
64
Future Value of an Annuity
Annuity- string of deposits with constant value and
fixed interval.
0             1                2            3

\$0            \$100           \$100           \$100
Compute FV3
How much would this account have in it at the end of 3
years if interest were earned at a rate of 8% annually?

–100.00

N   I/YR PV PMT FV
3    8        -100
65
Future Value of an Annuity
Annuity- string of deposits with constant value and
fixed interval.
0               1              2               3

\$0              \$100          \$100              \$100
Compute FV3
How much would this account have in it at the end of 3
years if interest were earned at a rate of 8% annually?

324.64
NOTE:
PV = 0 since the cashflow
in time period 0 = \$0       N   I/YR PV PMT FV
3    8       -100   ?
66
Future Value of an Annuity
Example
Susan is able to save \$980/yr for retirement. She
makes these deposits at the end of each year. If she
invests her savings at 12% compounded annually,
how much will she have upon retirement in 45
years?
67
Future Value of an Annuity
Example
Susan is able to save \$980/yr for retirement. She
makes these deposits at the end of each year. If she
invests her savings at 12% compounded annually,
how much will she have upon retirement in 45
years?
0     1      2     3      44     45

\$980   \$980   \$980   \$980   \$980
68
Future Value of an Annuity
Example
Susan is able to save \$980/yr for retirement. She
makes these deposits at the end of each year. If she
invests her savings at 12% compounded annually,
how much will she have upon retirement in 45
years?
0     1      2     3      44        45

\$980   \$980   \$980   \$980     \$980

1,331,065.43

N    I/YR PV PMT FV

45 12          -980   ?
69
Future Value of an Annuity
Example #1a
Susan will make equal quarterly payments totaling
\$980/yr for retirement. She makes these deposits at
the end of each quarter. If she invests her savings at
12% compounded quarterly, how much will she have
upon retirement in 45 years?
0            1             2              45

P/Yr = 1

\$245           1,661,944.10

N     I/YR PV PMT FV

180    3        -245    ?
70
Present Value of an Annuity
How much would the following cash flows be worth to you
today if you could earn 8% on your deposits?
0            1             2             3

\$0            \$100          \$100         \$100
71
Present Value of an Annuity
How much would the following cash flows be worth to you
today if you could earn 8% on your deposits?
0             1              2                 3

\$0             \$100           \$100           \$100
\$92.60 \$100/(1.08)
\$100 / (1.08)2
\$85.73
\$100 / (1.08)3
\$79.38
\$257.71

257.71

N   I/YR PV PMT FV

3    8   ? -100
72
Present Value of an Annuity
Loan Amortization
Borrow \$1,000 today, how much would the annual
payments be if you are required to repay in two
years and the interest rate is 10%?

–576.19

N   I/YR PV PMT FV

2    10 1,000 ?
73
Present Value of an Annuity
Example #1a
Bob borrows \$5,000 from his children to purchase a
used car. He agrees to make payments at the end of
each month for the next 5 years. If the interest rate
on this loan is 6%, what is the amount of the
payments?
74
Present Value of an Annuity
Example #1a
Bob borrows \$5,000 from his children to purchase a
used car. He agrees to make payments at the end of
each month for the next 5 years. If the interest rate
on this loan is 6%, what is the amount of the
payments?
0             1                   5

\$5,000
75
Present Value of an Annuity
Example #1a
Bob borrows \$5,000 from his children to purchase a
used car. He agrees to make payments at the end of
each month for the next 5 years. If the interest rate
on this loan is 6%, what is the amount of the
payments?
0             1                   5

\$5,000

–96.66

N I/YR PV PMT FV

60 0.5 5,000 ?
76
Present Value of an Annuity
Example #1a
Bob borrows \$5,000 from his children to purchase a
used car. He agrees to make payments at the end of
each month for the next 5 years. If the interest rate
on this loan is 6%, what is the amount of the
payments?
0             1                   5

\$5,000

–96.66

N I/YR PV PMT FV

60 0.5 5,000 ?
77
Annuity Due
Two Types of Annuities
Ordinary Annuity - Payments (or deposits) occur at
the end of the period
0                  1                   2      FV = \$205
\$0                \$100               \$100

Annuity Due - Payments (or deposits) occur at the
beginning of the period

0                  1                   2

\$100                 \$100             FV = ?
Each payment (or deposit) for an annuity due earns one
78
Annuity Due
Solving Annuity Due
Annuity Due - Payments (or deposits) occur at the
beginning of the period

0                 1                  2

\$100             \$100              FV = ?

FV AD = FV (ordinary) (1+i)

PV AD = PV (ordinary) (1+i)
79

0.00                                – 215.25
BEGIN                                BEGIN

P/YR
N   I/YR PV PMT FV                  N   I/YR PV PMT FV

2    5         100   ?
CLEAR ALL
INPUT

7      8           9     
4      5           6     x
1
1      2           3     –
2        BEG/END              DISP
0      .           =     +
80
Problem #1
Compute the monthly payments on a 30 year
mortgage for a \$120,000 loan at 8% annual interest,
compounded monthly.
81
Problem #2
You have determined that your budget will only allow
you to make a \$700 monthly mortgage payment. If
interest rates are currently 6% and mortgage terms
are typically 30 years, what price range home should
you be searching for if your downpayment is
\$15,000?

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