Introductory lecture on the time value of money for non-finance majors.

2.  Calculators must be set to 4 decimal
places
 Calculators must be set to 1 payment per
year

3. Chapter 3
Understanding The Time Value of
Money:

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)

9. 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

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?

12. No financial calculator
 10 * 1.05 to the 10th
 10(1.05)10

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

14. Financial Calculator….
 PV = -10 (DOLLARS)
 I/Y = 5 (PERCENT)
 N = 10 (YEARS/PERIODS)
 COMPUTE FV (FUTURE VALUE)

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?

17. No financial calculator
 100 * 1.12 to the 20th
 100(1.12)20

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

19. Financial Calculator….
 PV = -100 (DOLLARS)
 I/Y = 12 (PERCENT)
 N = 20 (YEARS/PERIODS)
 COMPUTE FV (FUTURE VALUE)

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.

24. Future Value Equation
FV = PV(1 + i)n

25. 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)?

26. Financial Calculators
 PV = -1000, N=15, I/Y = 11; CPT FV =
$4,784.58

27. Practice Problems:
 What is the future value (FV) of $1,500
after 20 years if it is invested in an account
earning 8% annually (APR)?

28. Financial Calculators
 PV = -1500, N = 20, I/Y = 8; CPT FV =
$6,991.44

29. Bringing your money back from 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.

32. Present Value Equation
PV = FV[1/(1 + i)n]

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

35. Solution
PV = FV[1/(1 + i)n]
PV = -100,000[1/(1.10) 5]
PV = $62,092

36. FINANCIAL CALCULATORS
 FV = -100,000
N=5
 I/Y = 10
 CPT PV = 62,092

37. Interest’s enemy: Inflation
 An economic condition in which rising
prices reduce the purchasing power of
money.

38. Inflation adjusted interest rate (i*)
Substitute i* for i during PV and FV formulas

39.  I = the interest rate
 R = inflation rate

40. Inflation adjusted interest rate (i*)
FV = PV(1 + i*)n
Controlling for inflation
PV = FV[1/(1 + i*)n]
Controlling for inflation

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

43. Next class…
 Chapter 3 part 2