ALAN ANDERSON, Ph.D.
     ECI RISK TRAINING
www.ecirisktraining.com
For free problem sets based on this material
along with worked-out solutions, write to
info@ecirisktraining.com. To learn ...
The time value of money is one of the most
fundamental concepts in finance; it is based
on the notion that receiving a sum...
The four basic time value of
 money concepts are:

 future value of a sum
 present value of a sum
 future value of an a...
If a sum is invested today, it will earn interest
and increase in value over time. The value that
the sum grows to is know...
The future value of a sum depends on
the interest rate earned and the time
horizon over which the sum is invested.

This i...
where:

 FVN     = future value of a sum
         invested for N periods
 I       = periodic rate of interest
 PV      = t...
Suppose that a sum of $1,000 is invested for
four years at an annual rate of interest of 3%.
What is the future value of t...
In this case,

     N=4
     I=3
     PV = $1,000




                (c) ECI RISK TRAINING 2009
                    www.e...
Using the future value formula,


    FVN = PV(1+I)N
    FV4 = 1,000(1+.03)4
    FV4 = 1,000(1.125509)
    FV4 = $1,125.51...
The present value of a sum is the amount
that would need to be invested today in
order to be worth that sum in the future....
The formula for computing the
present value of a sum is:


           FVN
    PV =
         (1 + I ) N




               ...
How much must be deposited in a bank
account that pays 5% interest per year in
order to be worth $1,000 in three years?


...
In this case,

           N=3
           I=5
           FV3 = $1,000




                (c) ECI RISK TRAINING 2009
      ...
FVN         1, 000
PV =            =
     (1 + I ) N
                  (1.05) 3



     1, 000
   =        = $863.84
     ...
An annuity is a periodic stream of
equally-sized payments.

The two basic types of annuities are:

       ordinary annuit...
With an ordinary annuity, the first
payment takes place one period in
the future.

With an annuity due, the first
payment ...
The formulas used to compute the
future value and present value of a
sum can be easily extended to the
case of an annuity....
The formula for computing the future
value of an ordinary annuity is:


           ⎡ (1 + I ) − 1 ⎤           N
FVAN = PMT...
where:



 FVAN    = future value of an
         N-period ordinary annuity

 PMT     = the value of the
         periodic ...
Suppose that a sum of $1,000 is invested at
the end of each of the next four years at an
annual rate of interest of 3%. Wh...
In this case,

     N=4
     I=3
     PMT = $1,000




                (c) ECI RISK TRAINING 2009
                    www....
Using the formula,



           ⎡ (1 + I ) − 1 ⎤              N
FVAN = PMT ⎢              ⎥
           ⎣       I      ⎦

...
⎡ (1 + .03) − 1 ⎤
                         4
FVA4 = 1,000 ⎢               ⎥ = $4,183.63
             ⎣       .03     ⎦



...
The future value of the annuity can
also be obtained by computing the
future value of each term and then
combining the res...
1,000(1.03)3 + 1,000(1.03)2 +
1,000(1.03)1 + 1,000(1.03)0

= 1,092.73 + 1,060.90 +
  1,030.00 + 1,000.00

= $4,183.63



 ...
The future value of an annuity due
is computed as follows:

   FVAdue = FVAordinary(1+I)




                      (c) ECI...
Referring to the previous example, the
future value of an annuity due would be:

   4,183.63(1+.03) = $4,309.14




      ...
The formula for computing the present
value of an ordinary annuity is:


              ⎡      1                           ...
where:



 PVAN    = future value of an
         N-period ordinary annuity

 PMT     = the value of the
         periodic ...
How much must be invested today in a bank
account that pays 5% interest per year in order
to generate a stream of payments...
In this case,

     N=3
     I=5
     PMT = $1,000




                (c) ECI RISK TRAINING 2009
                    www....
Using the formula,


              ⎡      1                             ⎤
                1−
              ⎢ (1 + I )N    ...
⎡       1    ⎤
                1−
              ⎢ (1 + .05)3 ⎥
PVA3 = 1, 000 ⎢            ⎥ = $2, 723.25
              ⎢  ...
The present value of the annuity can
also be obtained by computing the
present value of each term and then
combining the r...
1,000(1.05)-3 + 1,000(1.05)-2 + 1,000(1.05)-1
= 863.84 + 907.03 + 952.38
= $2723.25




                       (c) ECI RIS...
The present value of an annuity
due is computed as follows:

   PVAdue = PVAordinary(1+I)




                    (c) ECI ...
Referring to the previous example, the
present value of an annuity due would be:

   2,723.25(1+.05) = $2,859.41




     ...
Upcoming SlideShare
Loading in...5
×

Time Value Of Money Part 1

8,340

Published on

The Time Value of Money

Published in: Economy & Finance, Business
4 Comments
8 Likes
Statistics
Notes
No Downloads
Views
Total Views
8,340
On Slideshare
0
From Embeds
0
Number of Embeds
3
Actions
Shares
0
Downloads
1,400
Comments
4
Likes
8
Embeds 0
No embeds

No notes for slide

Time Value Of Money Part 1

  1. 1. ALAN ANDERSON, Ph.D. ECI RISK TRAINING www.ecirisktraining.com
  2. 2. For free problem sets based on this material along with worked-out solutions, write to info@ecirisktraining.com. To learn about training opportunities in finance and risk management, visit www.ecirisktraining.com (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 2
  3. 3. The time value of money is one of the most fundamental concepts in finance; it is based on the notion that receiving a sum of money in the future is less valuable than receiving that sum today. This is because a sum received today can be invested and earn interest. (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 3
  4. 4. The four basic time value of money concepts are:  future value of a sum  present value of a sum  future value of an annuity  present value of an annuity (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 4
  5. 5. If a sum is invested today, it will earn interest and increase in value over time. The value that the sum grows to is known as its future value. Computing the future value of a sum is known as compounding. (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 5
  6. 6. The future value of a sum depends on the interest rate earned and the time horizon over which the sum is invested. This is shown with the following formula: FVN = PV(1+I)N (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 6
  7. 7. where: FVN = future value of a sum invested for N periods I = periodic rate of interest PV = the present or current value of the sum invested (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 7
  8. 8. Suppose that a sum of $1,000 is invested for four years at an annual rate of interest of 3%. What is the future value of this sum? (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 8
  9. 9. In this case, N=4 I=3 PV = $1,000 (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 9
  10. 10. Using the future value formula, FVN = PV(1+I)N FV4 = 1,000(1+.03)4 FV4 = 1,000(1.125509) FV4 = $1,125.51 (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 10
  11. 11. The present value of a sum is the amount that would need to be invested today in order to be worth that sum in the future. Computing the present value of a sum is known as discounting. (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 11
  12. 12. The formula for computing the present value of a sum is: FVN PV = (1 + I ) N (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 12
  13. 13. How much must be deposited in a bank account that pays 5% interest per year in order to be worth $1,000 in three years?
 (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 13
  14. 14. In this case, N=3 I=5 FV3 = $1,000 (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 14
  15. 15. FVN 1, 000 PV = = (1 + I ) N (1.05) 3 1, 000 = = $863.84 1.1576 (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 15
  16. 16. An annuity is a periodic stream of equally-sized payments. The two basic types of annuities are:  ordinary annuity  annuity due (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 16
  17. 17. With an ordinary annuity, the first payment takes place one period in the future. With an annuity due, the first payment takes place immediately. (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 17
  18. 18. The formulas used to compute the future value and present value of a sum can be easily extended to the case of an annuity. (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 18
  19. 19. The formula for computing the future value of an ordinary annuity is: ⎡ (1 + I ) − 1 ⎤ N FVAN = PMT ⎢ ⎥ ⎣ I ⎦ (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 19
  20. 20. where: FVAN = future value of an N-period ordinary annuity PMT = the value of the periodic payment (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 20
  21. 21. Suppose that a sum of $1,000 is invested at the end of each of the next four years at an annual rate of interest of 3%. What is the future value of this ordinary annuity? (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 21
  22. 22. In this case, N=4 I=3 PMT = $1,000 (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 22
  23. 23. Using the formula, ⎡ (1 + I ) − 1 ⎤ N FVAN = PMT ⎢ ⎥ ⎣ I ⎦ (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 23
  24. 24. ⎡ (1 + .03) − 1 ⎤ 4 FVA4 = 1,000 ⎢ ⎥ = $4,183.63 ⎣ .03 ⎦ (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 24
  25. 25. The future value of the annuity can also be obtained by computing the future value of each term and then combining the results: (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 25
  26. 26. 1,000(1.03)3 + 1,000(1.03)2 + 1,000(1.03)1 + 1,000(1.03)0 = 1,092.73 + 1,060.90 + 1,030.00 + 1,000.00 = $4,183.63 (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 26
  27. 27. The future value of an annuity due is computed as follows: FVAdue = FVAordinary(1+I) (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 27
  28. 28. Referring to the previous example, the future value of an annuity due would be: 4,183.63(1+.03) = $4,309.14 (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 28
  29. 29. The formula for computing the present value of an ordinary annuity is: ⎡ 1 ⎤ 1− ⎢ (1 + I )N ⎥ PVAN = PMT ⎢ ⎥ ⎢ I ⎥ ⎢ ⎣ ⎥ ⎦ (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 29
  30. 30. where: PVAN = future value of an N-period ordinary annuity PMT = the value of the periodic payment (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 30
  31. 31. How much must be invested today in a bank account that pays 5% interest per year in order to generate a stream of payments of $1,000 at the end of each of the next three years?
 (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 31
  32. 32. In this case, N=3 I=5 PMT = $1,000 (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 32
  33. 33. Using the formula, ⎡ 1 ⎤ 1− ⎢ (1 + I )N ⎥ PVAN = PMT ⎢ ⎥ ⎢ I ⎥ ⎢ ⎣ ⎥ ⎦ (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 33
  34. 34. ⎡ 1 ⎤ 1− ⎢ (1 + .05)3 ⎥ PVA3 = 1, 000 ⎢ ⎥ = $2, 723.25 ⎢ .05 ⎥ ⎢ ⎣ ⎥ ⎦ (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 34
  35. 35. The present value of the annuity can also be obtained by computing the present value of each term and then combining the results: (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 35
  36. 36. 1,000(1.05)-3 + 1,000(1.05)-2 + 1,000(1.05)-1 = 863.84 + 907.03 + 952.38 = $2723.25 (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 36
  37. 37. The present value of an annuity due is computed as follows: PVAdue = PVAordinary(1+I) (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 37
  38. 38. Referring to the previous example, the present value of an annuity due would be: 2,723.25(1+.05) = $2,859.41 (c) ECI RISK TRAINING 2009 www.ecirisktraining.com 38
  1. A particular slide catching your eye?

    Clipping is a handy way to collect important slides you want to go back to later.

×