1. “Don't waste your time with explanations:
people only hear what they want to hear.”
Paulo Coelho

3. Time Value Of Money
 The Interest Rate
 Simple Interest
 Compound Interest
 Amortizing a Loan

4. Time Value Of Money
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!!

5. Time Value Of Money
Why TIME?
Why is TIME such an important element in
your decision?
TIME allows you the opportunity to postpone
consumption and earn INTEREST.

6. Types of Interest
INTEREST
(Price of Money)
Simple
Interest
Compound
Interest
Single Amount
Annuity
Ordinary
Annuity
Annuity Due
Perpetuity

7. Types of Interest

Simple Interest
Interest paid (earned) on only the principal amount, or
principal borrowed (lent).
Formula:
SI =(Po)(i)(n)
 Assume that you deposit $1,000 in an account earning
7% simple interest for 2 years. What is the accumulated
interest at the end of the 2nd year?
SI = (Po)(i)(n)
= $1000(0.07)(2)
s
= $140

8. Types of Interest

Simple Interest (FV)
 What is the Future Value (FV) of the deposit?
FV = Po+SI
= $1000+$140
=$1140
Future Value is the value at some future time of a present
amount of money, or a series of payments, evaluated at a
given interest rate.

9. Types of Interest

Simple Interest (PV)
 What is the Present Value (PV) of the previous
problem?
The Present Value is simply the $1,000 you originally
deposited. That is the value today!
Present Value is the current value of a future
amount of money, or a series of payments, evaluated
at a given interest rate.

10. Types of Interest
Compound Interest
Interest paid (earned) on any previous interest earned, as
well as on the principal borrowed (lent).
Example:
Assume that you deposit $1,000 at a compound
interest rate of 7% for 2 years.
0
7%
1
2
$1,000
FV2

11. Types of Interest
Future Value Single Deposit
FV1 = P0 (1+i)1
= $1,000 (1.07)
= $1,070
Compound Interest
You earned $70 interest on your $1,000 deposit
over the first year.This is the same amount of interest
you would earn under simple interest.

12. Types of Interest
Future Value Single Deposit
FV1 = P0 (1+i)1
= $1,000 (1.07)
= $1,070
FV2 = FV1 (1+i)1
= P0 (1+i)(1+i)
= $1,000(1.07)(1.07)
= P0 (1+i)2 = $1,000(1.07)2
= $1,144.90
You earned an extra $4.90 in Year 2 with compound over
simple interest.

13. Types of Annuities
Annuity:
A series of equal payments or receipts occurring
over a specified number of periods.
Ordinary Annuity:
In an ordinary annuity payments or receipts occur
at the end of each period.
Annuity Due:
In an annuity due payments or receipts occur at
the beginning of each period.

14. Types of Annuities
Ordinary Annuity (FV):
FVA= R(FVIFAi,n)
FVA= R[(1+i)ᵑ-1/i]
Activity:
If R=$1000, i= 8%, n= 3 years. Calculate future value
of ordinary annuity?
FVA= R[(1+i)ᵑ-1/i]
FVA= $1000[(1.08)³-1/(0.08)]
FVA= $3246

15. Types of Annuities
Ordinary Annuity (PV):
PVA= R(PVIFAi,n)
PVA= R[1-[1/(1+i)ᵑ]/i]
Activity:
Periodic receipts of $1000 at the end of each year ,
discount rate= 8%, n= 3 years. Calculate present value
ordinary annuity?
PVA= R[1-[1/(1+n)ᵑ]/i]
PVA= $1000 [1-[1/(1.08)³]/(0.08)]
PVA= $2577

16. Types of Annuities
Annuity Due (FV):
FVAD= R(FVIFAi,n)(1+i)
FVAD= R[(1+i)ᵑ-1/i](i+i)
Activity:
R=$1000, i= 5%, n= 5 years, Calculate future value of
annuity due?.
FVAD= R[1-[1/(1+n)ᵑ]/i] (1+i)
FVAD=$1000 [1-[1/(1.05)^5]/(0.05)](1.05)
FVAD= $5802.3

17. Types of Annuities
Annuity Due (PV):
PVAD= (1+i) (R) (PVIFAi,n)
PVAD= (1+i) (R) [1-[1/(1+i)ᵑ]/i]
Activity:
R=$1000, i= 8%, n= 3 years, Calculate present value
of annuity due?.
PVAD= (1+i) (R) [1-[1/(1+i)ᵑ]/i]
PVAD=(1.08) ($1000) [1-[1/(1.08)³]/(0.08)]
PVAD= $ 2783.16

18. Types of Annuities
Perpetuity:
An ordinary annuity whose payments or receipts
continue forever.
PVA
oo
=
R/I
Activity:
R=$1000, I = 5%,Calculate Perpetuity annuity?
PVA = R/I
PVA = $1000/0.05
PVA = $20000
oo
oo
oo

19. Amortizing A Loan
A table showing the repayment schedule of interest
and principal necessary to pay off a loan by maturity.
Activity:
PV= $10,000, i= 14% compounded annual, n= 4 years,
R=?
PV= R (PVIFAi,n)
$10,000= R (PVIFA14%,4)
$10,000 = R (2.914)
R= $10,000/2.914
R= $3432

20. Amortizing A Loan
End of Year
Installments
Interest
Principal
0
Amount Owing
At Year End
$10,000
1
$3432
$10000x 14%
=$1400
$2032
$7968
2
$3432
$7968x 14%
=$1116
$2316
$5652
3
$3432
$5652x 14%
=$791
$2641
$3011
4
$3432
$3011x 14%
=$421
$3011
-
$13,728
$3728
$10,000