4. Time Value of Money
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.
5. Interest and Compound Interest
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.
Inflation (r) – is when rising prices reduce
the purchase power of money.
6. The effect of 3% interest on a
one time deposit of $100
Reminders……3% = .03 in decimal form
On your calculator hit the 3 key and then
hit the % key (4th row from the top left
hand side)
7. 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)]
$103
8. Or in one easy step:
Your deposit ($X) multiplied by (1 + the
interest rate—in decimal form) = new acct.
balance
= $X(1 + i) = new account balance
= $100(1.03) = $103
$X + $X(i) = $X(1 + i)
10. In other words (short form)
X(1 + i)3 = X4 OR
X(1 + i)n
X = $$ deposit
I = % interest rate
Where n = number of periods you are
compounding
11. 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?
How much will you have in savings if you
deposit $100 in an account earning 12%
compounded annually for 20 years?
13. With your financial calculator you enter the
number and then tell it where to go…..
Key in -10 then hit the PV key
Key in 5 then hit the i/y key (don’t change
to decimal it does it for you)
Key in 10 hit the N key
Hit CPT FV key to show answer
15. $-16.28
***your answer will show up as a negative
number. That is expected because the
$10 was an outflow of cash from one’s
current consumption to one’s retirement
account. If you don’t want your answer to
show up as negative then you have to
remember to make the PV negative.
16. Practice problems
How much will you have in savings if you
deposit $100 in an account earning 12%
compounded annually for 20 years?
18. With your financial calculator you enter the
number and then tell it where to go…..
Key in -100 then hit the PV key
Key in 12 then hit the i/y key (don’t change
to decimal it does it for you)
Key in 20 hit the N key
Hit CPT FV key to show answer
20. $-964.63
***your answer will show up as a negative
number. That is expected because the
$10 was an outflow of cash from one’s
current consumption to one’s retirement
account. If you don’t want your answer to
show up as negative then you have to
remember to make the PV negative.
21. The Rule of 72
Estimates how many years an investment
will take to double in value
Number of years to double =
72 / annual compound growth rate (%)
Example -- 72 / 8 = 9 therefore, it will
take 9 years for an investment to double in
value if it earns 8% annually
22. Determining the Future Value of
your Money over time
Future value (FV) is the value to which
your money will grow at a specific
compounding interest rate (i).
Future value is hypothetically moving your
money forward (n) numbers of periods
(days, months, years).
23. Future Value Equation
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 today’s dollars, of a sum of
money
This equation is used to determine the value of
an investment at some point in the future.
30. 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)
―inverse compounding‖
31. Present Value Equation
PV = FV(1/(1 + i)n)
PV = the present value, in today’s 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 today’s value
of some future sum of money.
34. 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
today, how much will he receive
41. 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!!!!
42. Summary
FV = PV (1 + i)n
What your money will grow to be
PV = FV (1/(1 + i)n
What your future money is worth today
Inflation adjusted interest rate: (i*)
Substituting i* for i when controlling for
inflation