What is the 'Time Value of Money - TVM' The time value of money (TVM) is the idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. TVM is also referred to as present discounted value. BREAKING DOWN 'Time Value of Money - TVM' Money deposited in a savings account earns a certain interest rate. Rational investors prefer to receive money today rather than the same amount of money in the future because of money's potential to grow in value over a given period of time. Money earning an interest rate is said to be compounding in value. BREAKING DOWN 'Compound Interest' Compound Interest Formula Compound interest is calculated by multiplying the principal amount by one plus the annual interest rate raised to the number of compound periods minus one.The total initial amount of the loan is then subtracted from the resulting value.

1. Time Value of Money
Lecture 3

2. The Time Value of Money
• The Interest Rate
• Simple Interest
• Compound Interest
• Amortizing a Loan

3. Why Time?
• Because it provides us with an opportunity to put
our money to work and start to earn interest from
now on.
• TIME allows you the opportunity to postpone
consumption and earn INTEREST.

4. The Interest Rate
• Which would you prefer -- $10,000 today or $10,000 in
5 years?
Obviously, $10,000 today.
You already recognize that there is TIME VALUE TO
MONEY
Because you can invest it today and start to earn
Interest.
• In a world where cash flows are certain then rate of
return can be used to express the time value of money
and rate of interest allows us to to value cash flows.

5. Types of Interest
• Simple Interest
• Interest paid (earned) on only the original amount,
or principal borrowed (lent).
• Dollar amount of simple interest is a function of
three variables.
1:original amount borrowed or lent
2:Interest rate for the time period
3:Number of time periods
SI = P0(i)(n)

6. Simple Interest Example
• Assume that you deposit $1,00 in an account
earning 8% simple interest for 10 years. What is the
accumulated interest at the end of the 10th year?
• SI = P0(i)(n)
SI=100(.08)(10)=80

7. Simple Interest (FV)
• Future Value or terminal value
• The value at some future time of a present amount of
money or a series of payments evaluated at a given
interest rate.
• For any simple interest the future value of an account
at the end of n periods
• FVn= P0 + SI= P0 +P0 (i)(n)…………………………(1)
• Or we can write this as
• FVn= = P0 [1+(i)(n)]………………………………..(2)

8. Future Value
• What is the Future Value (FV) of the deposit?
• FV = P0 + SI
• = $1,00 + $80
• = $180
• So FV= 100+[100(.08)(10)]=$180
Or
FVn=100[1+(.08)(10)]
=180

9. Simple Interest (PV)
• Sometimes we need to proceed in opposite direction.
• That is we know the FV of deposit at interest rate deposited for
“n” years but we don’t know the principal originally invested…..so
re arrangement of equation 2 is required to get present value.
• FVn= = P0 [1+(i)(n)]…………..(2)
• Pv0
P0 =FVn/ [1+(i)(n)]
Present Value is the current value of a future amount of money, or
a series of payments, evaluated at a given interest rate.
So PV is the present value is the original amount which was
deposited which is 100.

10. Compound Interest
• Interest paid(earned) on any previous interest
earned as well as on principal borrowed(lent)
• Interest paid on an investment is periodically added
to the principal.so this is interest on interest or
compounding.

11. Future Value
Single Deposit
• Assume that you deposit $1,00 at a compound
interest rate of 8% for 3 years.
• So at the end of year 2nd
• 0 1 2 3
• $1,00
FV3

12. Future Value
Single Deposit (Formula)
• FV1 = P0 (1+i)1 = $1,00 (1.08)
= $1,08
Compound Interest
You earned $8 interest on your $1,00 deposit over
the first year.
This is the same amount of interest you would earn
under simple interest.

13. Single Deposit
• FV2 = FV1 (1+i)1
= P0 (1+i)(1+i) = $1,00(1.08)(1.08)
= P0 (1+i)2 = $1,00(1.08)2
= $1,16.64
• The initial deposit have grown to 108 at end of year
one with 8% return. Going to second year 108
becomes 116.64 as $8 interest earned on initial
deposit of $100 and $0.64 is earned on the $8
interest credited to our account at the end of first
year.in other words interest is earned on previously
earned interest. Hence the name is compound
interest

14. Single Deposit
• P3 (1+i)(1+i)(1+i) = $1,00(1.08)(1.08)(1.08)
= P0 (1+i)3 = $1,00(1.08)3
= $125.97

15. General Future Value Formula
FV1 = P0(1+i)1
FV2 = P0(1+i)2
General Future Value Formula:
FVn = P0 (1+i)n
or FVn = P0 (FVIFi,n)
FVIFi,n (future value interest factor at i% for n
Periods or terminal value interest factor)
=
(1+i)n

16. Example
• Julie Miller wants to know how large her deposit of
$10,000 today will become at a compound annual
interest rate of 10% for 5 years.
• Calculation based on general formula:
• FVn = P0 (1+i)n
• FV5 = $10,000 (1+ 0.10)5
• = $16,105.10
• Calculation based on Table I:
• FV5 = $10,000 (FVIF10%, 5)
= $10,000 (1.611)
= $16,110 [Due to Rounding]

17. Present Value Single Deposit (Graphic)
• PV or discounted value(interest rate used to
convert future values to present values)
• We all realize that a dollar today is worth more than
a dollar to be received after one, two or three years
from now. Calculating the present value of future
cash flows allows us to place all cash flows on a
current footing so that comparison can be made in
terms of today’s dollar.

18. Example
• Assume that you need $1,000 in 2 years. Let’s
examine the process to determine how much you
need to deposit today at a discount/interest rate of
7% compounded annually?
• 0 1 2
7% $1000
PV0 PV1

19. Formula
Lets drive PV from Future value formula
FVn = P0 (1+i)n
Re-arranging it
PV0 = P0 = FVn / (1+i)n or FVn [1/(1+i)n ]
General Present Value Formula:
or PV0 = FVn (PVIFi,n)
Note that the term [1/(1+i)n ] is simply the
inverse of future value of interest factor for “n”
periods.

20. Example Solution
• PV0 = FV2 / (1+i)2
• = $1,000 / (1.07)2
• = FV2 / (1+i)2 = $873.44
• So finally if we are promised to receive 1000
received today we would prefer to take 1000
today rather than after two years.

21. Unknown Interest Rate or discount rate
• Some times we are faced with a time value of
money in which we know both PV and FV as well as
number of time periods involved. What is unknown
is interest rate.
• Example:
• If Cesario invest $1000 today. he will receive $3000
in exactly 8 years. What is the compound
rate(discount)?

22. Example
• Lets start with future value formula
• FV8 = P0 (FVIFi,8)
$3000=$1000(FVIFi,8)
By re-arranging it
FVIFi,8 =$3000/$1000=3
If remember
(1+i)8 =3
(1+i) = 30.125 =1.1472
i=0.1472

23. Unknown Time periods
• Some times we know PV, FV and compound interest
rate but what we don’t know is the time period.so
again we can drive it using future value
formula…lets now jump on example.
• For how long will it take for a investment of $1000
to grow to $1900.if we invested it at a compound
annual interest rate of 10%?
• Lets start with basic future value formula.