economics notes by prof:muhammad irfan

2. INTEREST & EQUIVALENCE
MUHAMMAD IRFAN
Assistant Professor, Sarhad University, Peshawar.

3. INTEREST….
The amount paid by borrower to the lender for the use of capital.
Interest involves a transaction between those
people, firms or institutions
who have Surplus
and others who are in deficit in funds and require them
for their own use.

4. INTEREST…
Example: Loan
Parties
Lends the Money
Principal
Borrowers the Money OWES
(Debt)
to Lender

5. BorrowerLender
Earns (Income) from Borrower
i.e. Interest on the Principal
Borrower pays
Interest to Lender
Rate of
Interest:
Simple Interest…
Calculated on an ANNUAL or per annum
(PA) basis
Example: Loan

6. SIMPLE INTEREST
To find simple interest we use the following
formula:
I = prt
Interest
Principal
Interest rate
written as a
decimal
The amount of
time the money
is invested or
borrowed (years)

7. FIND THE INTEREST EARNED…
 Amjad has $750 in a savings account that
pays 3% simple interest. How much interest
will he earn in 4 years?
I = 750 x 3% x 4
Amjad will earn $90 interest in 4
years.

8. FIND THE INTEREST PAID…
 Adnan borrows $1,200 from the bank for a
Machine. The interest rate is 8% per year.
How much simple interest will he pay if he
takes 2 years to repay the loan?
I = 1,200 x 8% x 2
Adnan will pay $192 interest in 2
years.

9. FIND THE TOTAL PAID
 Asif charged $600 TV on his credit card with
an interest rate of 21%. How much money
will he owe after 9 months.
9 months is how many years? 9/12 = 0.75
years
I = 600 x 21% x 0.75 = $94.50 interest
Amount paid $600 + $94.50 = $694.50

10. EXAMPLE…
Invest $1000 at 10% simple
interest for one year.
Interest earned is?
Principal X Interest Rate $1000 * 10% /1 = $100
Invest $1000 at 10% simple
interest for six months.
Interest earned is?
Principal X Interest Rate $1000 * 10% $50/2 =
=
=

11. ANOTHER EXAMPLE…
Invest $1000 at 10% simple
interest for three months
Interest earned is?
Principal X Interest Rate =
$1000 X 10% $25
Invest $1000 at 10% simple
interest for one month.
Interest earned is?
Principal X Interest Rate = $1000 X 10% $8.33/12 =
/4=

12. trPI
“What is the formula that can be
used to calculate Simple
Interest?”
Principal Interest Rate Time
Four Elements are involved …
Interest
Formula
Principal Amount
(loan or investment)
Annual Rate
of SI
Amount
(paid or
received)
Time period
…expressed as a
fraction or a
multiple of a
year
I = Prt

13. Calculate the Interest earned
on $5000 invested at 4%
for 7 months.
Formula I = Prt
I = P * r * t
$5000 * .04 * 7 /12
I = $116.67

14. EARNING OF THE DAYS…
6 - 14
Formula I = Prt
Calculate the Interest earned
on $5000 invested
at 4.5% for
? .79 Days
I =$5000*.045 *79/365
I = $48.70

15. FURTHER…
We can ‘reorganize’ the formula to also
get each of the following separately:
•Principal
•Rate
•Time

16. USE OF THIS…
I
Prt
To help remember this…
we can place the formula into a triangle as follows…
Where variables are BESIDE
EACH OTHER this means to
MULTIPLYP*r*t
I
Prt
Where a variable is ABOVE
ANOTHER this means to DIVIDE

17. If you want to find P then
I
/rt
If you want to find r
then
I
/Pr
then
I
/P
tIf you want to find t
Using this tool!
I
Prt

18. 18
ECONOMIC DECISION COMPONENTS
 Where economic decisions are immediate,
we need to consider:
 Amount of Expenditure
 Taxes
….AND…..
 Where economic decisions occur over a
considerable period of time,
we need also to consider the consequences of;
Interest
Inflation

19. INTEREST AND EQUIVALENCE
Example: You borrowed $5,000 from a bank and you have to pay it back in 5
years. There are many ways the debt can be repaid. (i = 0.08)
Plan 1: At end of each year pay $1,000 principal plus interest due.
Plan 2: Pay interest due at end of each year and principal at end of five years.
Plan 3: Pay in five end-of-year payments ($1,252).
Plan 4: Pay principal and interest in one payment at end of five years.
All these plans are equivalent in the sense that the sum of all
outgoing cash flows at time 0 is $5,000.

20. PRESENT VALUE
 Plan 1: At end of each year pay $1,000 principal plus interest due
(a) (b) (c) (d) (e) (f)
Yr. Amnt. Owed Int. Owed Total Owed Princip. Total Payment
Begin. of Yr 0.08 * b b + c Payment
1 $5,000 $400 $5,400 $1,000 $1,400
2 $4,000 $320 $4,320 $1,000 $1,320
3 $3,000 $240 $3,240 $1,000 $1,240
4 $2,000 $160 $2,160 $1,000 $1,160
5 $1,000 $80 $1,080 $1,000 $1,080
$1,200 $5,000 $6,200

21. PRESENT VALUE
 Plan 2: Pay interest due at end of each year and principal at end of five years.
(a) (b) (c) (d) (e) (f)
Yr. Amnt. Owed Int. Owed Total Owed Princip. Total Payment
Begin. of Yr 0.08 * b b + c Payment
1 $5,000 $400 $5,400 $0 $400
2 $5,000 $400 $5,400 $0 $400
3 $5,000 $400 $ 5,400 $0 $400
4 $5,000 $400 $ 5,400 $0 $400
5 $5,000 $400 $ 5,400 $5,000 $5,400
$2,000 $5,000 $7,000

22. PRESENT VALUE
 Plan 3: Pay in five end-of-year payments
(a) (b) (c) (d) (e) (f)
Yr. Amnt. Owed Int. Owed Total Owed Princip. Total Payment
Begin. of Yr 0.08 * b b + c Payment
1 $5,000 $400 $5,400 $852 $1,252
2 $4,148 $332 $4,480 $920 $1,252
3 $3,228 $258 $3,485 $994 $1,252
4 $2,234 $179 $2,412 $1,074 $1,252
5 $1,160 $93 $1,252 $1,159 $1,252
$1,261 $5,000 $6,261

23. PRESENT VALUE
 Plan 4: Pay principal and interest in one payment at end of five years.
(a) (b) (c) (d) (e) (f)
Yr. Amnt. Owed Int. Owed Total Owed Princip. Total Payment
Begin. of Yr 0.08 * b b + c Payment
1 $5,000 $400 $5,400 $0 $0
2 $5,400 $432 $5,832 $0 $0
3 $5,832 $467 $6,299 $0 $0
4 $6,299 $504 $6,802 $0 $0
5 $6,802 $544 $7,347 $5,000 $7,347
$2,347 $5,000 $7,347
Compound Interest:
interest is charged on
the unpaid interest.

24. Economic Equivalence
 What do we mean by “economic
equivalence?”
 Why do we need to establish an economic
equivalence?
 How do we establish an economic
equivalence?

25. ECONOMIC EQUIVALENCE…
 Economic equivalence exists between cash
flows that have the same economic effect
and could therefore be traded for one
another.
 Even though the amounts and timing of the
cash flows may differ, the appropriate interest
rate makes them equal.

26.  If you deposit P dollars
today for N periods at
i, you will have F
dollars at the end of
period N.
N
F
P
0
N
iPF )1( 
EQUIVALENCE FROM PERSONAL FINANCING POINT OF VIEW
P F

27.  F dollars at the end of
period N is equal to a
single sum P dollars
now, if your earning
power is measured in
terms of interest rate i.
N
F
P
0
N
iFP 
 )1(
ALTERNATE WAY OF DEFINING EQUIVALENCE
N0

28. PRACTICE PROBLEM…
0 1 2 3 4 5
$2,042
5
F
0
At 8% interest, what is the equivalent worth
of $2,042 now 5 years from now?
If you deposit $2,042 today in a savings
account that pays 8% interest annually.
how much would you have at the end of
5 years?
=

29. SOLUTION…
5
$2,042(1 0.08)
$3,000
F  


30. EXAMPLE 2.2
$3,000$2,042
50
At what interest rate
would these two amounts be equivalent?
i = ?

31. Equivalence Between Two Cash Flows
 Step 1: Determine the
base period, say, year 5.
 Step 2: Identify the
interest rate to use.
 Step 3: Calculate
equivalence value.
$3,000$2,042
50
i F
i F
i F
   
   
   
6%, 042 1 0 06 733
8%, 042 1 0 08 000
10%, 042 1 0 10
5
5
5
$2, ( . ) $2,
$2, ( . ) $3,
$2, ( . ) $3,289

32. EXAMPLE - EQUIVALENCE
Various dollar amounts that will be economically equivalent
to $3,000 in 5 years, given an interest rate of 8%.
P= (A) divided by (one) plus rate of interest to the
power years.
0 1 2 3 4 5
P F
$2,042 $3,000$2,205 $2,382 $2,778$2,572
5
$3,000
$2,042
(1 0.08)
P  


33. Thank You…