Value Time of Money
Chapter 3
A dollar received today is worth more than
a dollar received in the future.
The sooner your money can earn interest,
the faster the interest can earn interest
the faster the interest can earn interest.
Understanding The Time Value of
Money:
Interest and Compound Interest
_______________________ (i) -- is the
return you receive for investing your
money.
Compound interest -- is the interest that
your investment earns on the interest that
your investment previously earned.
______________________ (r) is when
rising prices reduce the purchase power of
money.
The effect of 3% interest on a
one time deposit of $100
Deposit ($X)
+ Deposit ($X) times interest rate (i)
= new account balance
For example:
$100 ($X)
+ $ 3 [100 (.03) = $X(.03)]
$103
The effect of 3% interest on a
___________________ of $100
Reminders3% = .03 in decimal form
On your calculator hit the 3 key and then
hit the % key (4th row from the top left
hand side)
hand side)
Or in one easy step:
Your deposit ($X) multiplied by (1 + the
interest ratein decimal form) = new acct.
balance
= $X(1 + i) = new account balance
= $100(1.03) = $103
$X + $X(i) = $X(1 + i)
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The effect of compounding interest
over time (long form)
= $X1 + [$X1(i)] = $X2
= $X2 + [$X2(i)] = $X3
= $X3 + [$X3(i)] = $X4 .
= $100x1 + [$100x1(.03)] = $103x2
= $103x2 + [$103x2(.03)] = $106.09x3
= $106.09x3 + [$106.09x3(.03)] = $109.27x4
Practice problems
How much will you have in savings if you
deposit $10 and leave it in an account
earning 5% interest compounded annually
for 10 years?
for 10 years?
How much will you have in savings if you
deposit $100 in an account earning 12%
compounded annually for 20 years?
In other words (short form)
X(1 + i)3 = X4
X(1 + i)n
OR
X = $$ deposit
I = % interest rate
Where n = number of ____________________
you are compounding
No financial calculator
10 * 1.05 to the 10th
10(1.05)10
100 * 1.12 to the 20th
100(1.12)20
Financial Calculator.
PV = 10 (DOLLARS)
I/Y = 5 (PERCENT)
N = 10 (YEARS/PERIODS)
COMPUTE FV (FUTURE VALUE)
PV = 100 (DOLLARS)
I/Y = 12 (PERCENT)
N = 20 (YEARS/PERIODS)
COMPUTE FV (FUTURE VALUE)
With your financial calculator you enter the
number and then tell it where to go..
Key in 10 then hit the PV key
in then hit the i/y key (don change
Key in 5 then hit the i/y key (dont change
to decimal it does it for you)
Key in 10 hit the N key
Hit CPT FV key to show answer
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The Rule of ____________
$-16.28
$-964.63
***your answer will show up as a negative
number. That is expected because the $10 was
number. That is expected because the $10 was
an outflow of cash from ones current
consumption to ones retirement account. If you
dont want your answer to show up as negative
then you have to make the PV negative.
Estimates how many years an investment
will take to double in value
Number of years to double =
72
72 / annual compound growth rate (%)
(%)
Example -- 72 / 8 = 9 therefore, will
take it 9 years for an investment to double in
value if it earns 8% annually
Determining the Future Value of
your Money over time
Future Value Equation
Future value (FV) is the value to which
your money will grow at a specific
compounding ___________________ rate
(i)
(i).
Future value is hypothetically moving your
money forward (n) numbers of periods
(days, months, years).
Future Value Equation
FV = PV(1 + i)n
FV = PV(1 + i)n
FV = the future value of the investment at the end of
(n) numbers of periods
i = the annual percentage (interest) rate (APR)
PV = the present value, in todays dollars, of a sum of
money
This equation is used to determine the value of
an investment at some point in the future.
Practice Problems:
What is the future value (FV) of $1,000 at
the end of 15 years if it is invested in an
account bearing 11% annually (APR)?
What is the future value (FV) of $1,500
after 20 years if it is invested in an account
earning 8% annually (APR)?
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Financial Calculators
Bringing your money back from the
future.
PV = 1000, N=15, I/Y = 11; CPT FV =
$4,784.58
PV = 1500, N = 20, I/Y = 8; CPT FV =
$6,991.44
Determining the Present Value
of your money
Present Value (PV) Is hypothetically
moving dollars from the future back into
the present at a specific interest rate (i) for
a specific number of periods (n)
specific number of periods (n)
_____________________compounding
Present Value Equation
PV = FV(1/(1 + i)n)
PV = the present value, in todays dollars, of a sum of
money
FV = the future value of the investment at the end of n
years
i = annual interest rate (%)
(%)
n = number of periods
This equation is used to determine todays value
of some future sum of money.
Present Value Equation
PV = FV[1/(1 + i)n]
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Practice Problems
Josh is due to receive his inheritance
($100,000) in 5 years. It is in an account
earning 10% annually. Josh wants his
money now If Josh withdraws his money
money now. If Josh withdraws his money
today, how much will he receive
FINANCIAL CALCULATORS
FV = 100,000
N=5
I/Y = 10
CPT PV = 62,092
Solution
PV = FV[1/(1 + i)n]
PV = 100,000[1/(1.10)5]
PV = $62,092
Interests enemy: ____________
An economic condition in which rising
prices reduce the purchasing power of
money.
Inflation adjusted interest rate (i*)
Substitute i* for i during PV and FV formulas
I = the interest rate
R = inflation rate
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Inflation adjusted interest rate (i*)
FV = PV(1 + i*)n
Controlling for inflation
PV = FV[1/(1 + i*)n]
In your financial calculator the I in I/Y is
now replaced with I* (the inflation adjusted
interest rate)
You MUST calculate the I* first!!!!
MUST calculate the I* first!!!!
Controlling for inflation
Summary
FV = PV (1 + i)n
Next class
Chapter 3 part 2
What your money will grow to be
PV = FV (1/(1 + i)n
What your future money is worth today
Wh
Inflation adjusted interest rate: (i*)
Substituting i* for i when controlling for
inflation
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