What is time value of money? Annuities, simple interest, compound interests, present value, future value, etc.

1. Time Value of Money

2. Would you prefer to
have 1 crore now or 1
crore 10 years from
now?
Would you prefer to
have 1 crore now or 1
crore 10 years from
now?

3. The Terminology of Time ValueThe Terminology of Time Value
 Present Value - An amount of money today, or the
current value of a future cash flow
 Future Value - An amount of money at some future
time period
 Period - A length of time (often a year, but can be a
month, week, day, hour, etc.)
 Interest Rate - The compensation paid to a lender (or
saver) for the use of funds expressed as a percentage
for a period (normally expressed as an annual rate)
 Present Value - An amount of money today, or the
current value of a future cash flow
 Future Value - An amount of money at some future
time period
 Period - A length of time (often a year, but can be a
month, week, day, hour, etc.)
 Interest Rate - The compensation paid to a lender (or
saver) for the use of funds expressed as a percentage
for a period (normally expressed as an annual rate)

4. Time Value of Money
• The value of money changes with change in
time.
• A rupee received today is more valuable than
a rupee received one year later.
– Present Value concept (PV concept)
– Future or Compounding Value concept (FV
concept)
• The value of money changes with change in
time.
• A rupee received today is more valuable than
a rupee received one year later.
– Present Value concept (PV concept)
– Future or Compounding Value concept (FV
concept)

5. Reasons for Time Preference of Money
• Uncertain future
• Risk involvement
• Present needs
• Return
• Uncertain future
• Risk involvement
• Present needs
• Return

6. Note: Annuity means series of constant cash flows starting from first year to
nth year (say up to 5th year, 10 years etc.).

7. Future Value of a Single Amount
Say that you put $1,000 into the bank
today. How much will you have after a
year? After two years? This kind of
problem is called a future value /
compounding problem.
Say that you put $1,000 into the bank
today. How much will you have after a
year? After two years? This kind of
problem is called a future value /
compounding problem.

8. Compounding vs. Simple Interest
• Compounding interest is defined as earning
interest on interest.
• Simple interest is interest earned on the
principal investment.
• Principal refers to the original amount of
money invested or saved
• Compounding interest is defined as earning
interest on interest.
• Simple interest is interest earned on the
principal investment.
• Principal refers to the original amount of
money invested or saved

9. Future Value of a Single Amount
You have Rs.1,000 today and you deposit it
with a financial institution, which pays 10
per cent interest compounded annually,
for a period of 3 years. What is the total
amount after 3 years?
You have Rs.1,000 today and you deposit it
with a financial institution, which pays 10
per cent interest compounded annually,
for a period of 3 years. What is the total
amount after 3 years?

10. Formula
FVn =PV×(1+k)n
FVn = Future value n years
PV = Present Value (cash today)
k = Interest rate per annum
n = Number of years for which compounding
is done
FVn =PV×(1+k)n
FVn = Future value n years
PV = Present Value (cash today)
k = Interest rate per annum
n = Number of years for which compounding
is done

11. If you deposit Rs.10,000 today in a bank
which pays 12% interest compounded
annually, how much will the deposit
grow to after 10 years and 12 years?
Example
If you deposit Rs.10,000 today in a bank
which pays 12% interest compounded
annually, how much will the deposit
grow to after 10 years and 12 years?

12. Doubling period
• How much time is required to double my
investment?
• The length of period which an amount is going
to take o double at a certain given rate of
interest.
• How much time is required to double my
investment?
• The length of period which an amount is going
to take o double at a certain given rate of
interest.

13. Rule of 72
72
Doubling Period = ---------------------
Rate of Interest
72
Doubling Period = ---------------------
Rate of Interest

14. If you deposit Rs.10,000 today at 6 per
cent rate of interest, in how many
years will this amount double?
Workout this with the rule of 72.
Example
If you deposit Rs.10,000 today at 6 per
cent rate of interest, in how many
years will this amount double?
Workout this with the rule of 72.

15. Rule of 69
69
Doubling Period = 0.35 + ---------------------
Rate of Interest
69
Doubling Period = 0.35 + ---------------------
Rate of Interest

16. If you deposit Rs.20,000 today at 6 per
cent rate of interest, in how many
years will this amount double?
Workout this with the rule of 69.
Example
If you deposit Rs.20,000 today at 6 per
cent rate of interest, in how many
years will this amount double?
Workout this with the rule of 69.

17. Multiple Compounding Periods
• Interest may have to be compounded more
than once a year.
• Example: Banks may allow interest on
quarterly or half yearly basis; or a company
may allow compounding of interest twice a
year.
• Interest may have to be compounded more
than once a year.
• Example: Banks may allow interest on
quarterly or half yearly basis; or a company
may allow compounding of interest twice a
year.

18. Formula
FVn =PV×(1+k/m)m x n
FVn = Future value n years
PV = Present Value (cash today)
k = Interest rate per annum
n = Number of years for which compounding
is done
m = Number of times compounding is done
during a year
FVn =PV×(1+k/m)m x n
FVn = Future value n years
PV = Present Value (cash today)
k = Interest rate per annum
n = Number of years for which compounding
is done
m = Number of times compounding is done
during a year

19. Calculate the compound vale of
Rs.10,000 at the end of 3 years at 12%
rate of interest when interest is
calculated on
– Yearly basis
– Half yearly basis
– Quarterly basis
Example
Calculate the compound vale of
Rs.10,000 at the end of 3 years at 12%
rate of interest when interest is
calculated on
– Yearly basis
– Half yearly basis
– Quarterly basis

20. Effective Vs. Nominal Rate
• Effective Interest rate: The percentage
rate of return on an annual basis. It
reflects the effect of intra-year
compounding. (Ex. 12.36%)
• Nominal Interest rate: Interest rate
expresses in monitory terms. (Ex. 12%)
• Effective Interest rate: The percentage
rate of return on an annual basis. It
reflects the effect of intra-year
compounding. (Ex. 12.36%)
• Nominal Interest rate: Interest rate
expresses in monitory terms. (Ex. 12%)

21. Formula
ERI = (1 + k/m)m – 1
ERI = Effective Rate of Interest
k = Nominal Rate of Interest
m = Frequency of compounding per year
ERI = (1 + k/m)m – 1
ERI = Effective Rate of Interest
k = Nominal Rate of Interest
m = Frequency of compounding per year

22. Example
A bank offers 8 per cent nominal rate of
interest on deposits. What is the effective
rate of interest if the compounding is done
i) half yearly
ii) quarterly &
iii) monthly
A bank offers 8 per cent nominal rate of
interest on deposits. What is the effective
rate of interest if the compounding is done
i) half yearly
ii) quarterly &
iii) monthly

23. Future Value of an Annuity
• Suppose you deposit Rs.1,000 annually in a
bank for 5 years and your deposits earn a
compound interest rate of 10 per cent. What
will be the value of this series of deposits (an
annuity) at the end of 5 years?
• Suppose you deposit Rs.1,000 annually in a
bank for 5 years and your deposits earn a
compound interest rate of 10 per cent. What
will be the value of this series of deposits (an
annuity) at the end of 5 years?

24. • 1000 (1.1)4 + 1000 (1.1)3 + 1000 (1.1)2 +
1000 (1.1)1 + 1000
• 1000 (1.4641) + 1000 (1.331) + 1000 (1.21) +
1000 (1.1) + 1000
• 6,105
• 1000 (1.1)4 + 1000 (1.1)3 + 1000 (1.1)2 +
1000 (1.1)1 + 1000
• 1000 (1.4641) + 1000 (1.331) + 1000 (1.21) +
1000 (1.1) + 1000
• 6,105

25. Formula
(1 + K)n – 1
FVAn = A -----------
K
FVAn = Future value of an Annuity n years
A = Constant periodic flow
k = Interest rate per period
n = duration of the annuity
(1 + K)n – 1
FVAn = A -----------
K
FVAn = Future value of an Annuity n years
A = Constant periodic flow
k = Interest rate per period
n = duration of the annuity

26. (1 +.1)5 – 1
• FVA = 1000 --------------------
.1
(1 +.1)5 – 1
• FVA = 1000 --------------------
.1

27. Present Value of a Single Amount
• Suppose someone promises to give you
Rs.1,000 three years hence. What is the
present value of this amount if the interest
rate is 10 per cent?
• Suppose someone promises to give you
Rs.1,000 three years hence. What is the
present value of this amount if the interest
rate is 10 per cent?

28. Formula
n
PV = FVn

29. Present Value of An Annuity
Suppose you expect to receive Rs.1,000
annually for 3 years, each receipt occurring at
the end of the year. What is the present value
of this stream of benefits I the discount rate is
10 per cent?
Suppose you expect to receive Rs.1,000
annually for 3 years, each receipt occurring at
the end of the year. What is the present value
of this stream of benefits I the discount rate is
10 per cent?

30. • 1000 (1/1.1) + 1000 (1/1.1)2 + 1000 (1/1.1)3
• 1000x.909 + 1000x.826 + 1000x.751
• 2486
• 1000 (1/1.1) + 1000 (1/1.1)2 + 1000 (1/1.1)3
• 1000x.909 + 1000x.826 + 1000x.751
• 2486