Finan cial mathe matic s
, Chapter 2 Simple interest & Simple discount
a
2.1. Simple interest
Interest price paid for the use of borrowed
money
• = .
who lender
Party borrows
pays interest to
-
•
- .
• Interest -
Calculated as a friction of the amount borrowed .
Friction Interest rate Expressed as % (0112--124)
per year
• = - .
•
simple interest :
calculated on principal amount borrowed .
Example
Simple in thrust is
computed on the
D principal for the entire
term of the loan &
is due @ the end of
term .
Formula
I. Prt
F- Interest paid @ end of term .
F- Principal
F-
/ total
Rate of interest
amount
.
borrowed
/ PV of loan .
b- =
Time in YEARS .
Interest rate per annum, then the term must be in
years
• =
or fraction thereof .
-
. .
We need to
change the months days or weeks to fraction
,
a
the months by the number of
of a
year by dividingCIZ) & weeks ÷ 52 &
months in a
year , ,
days ÷ 365 .
,2.1. Simple interest
The accumulated G)
Maturity
•
sum =
value
=
Future value
=
Accused principal .
@ end
" "
of term t is
given by :
5- Pcitrt )
5- Principal value + interest
5 =
PTI
s =
Pt Prt
Pcitrt)
≤ Date @ the end of term
5 =
@ which the debt is to
↳ law of multiplication over addition .
be
date
paid
.
= due date
/ maturity
i. abtac = a Cbtc )
q =P < .
b- I-
- . Plt Prt = Part )
[ =
rt
←
Exercise 2.1
5- Patris)
-
← Can turn basic formula
"
I =
Prt
"
inside
=
50004+1%0 ✗¥5 ) out .
The concept of PV is obtained
=
5000 (11-0,15×5%5) 4- enter as is on calc .
by basic formula for the sum of FV
"
S
"
= 125184,93 .
: 5- Pcltrt )
( Hrt ) gives :
Calculator dividing by factor
1) Setup 0 Do a Decimal
- - =
P=¥rt
2) Divide time by fraction
.
Save fraction
3) f- Amount that must be borrowed
To 90.1-365 ^
to accrue the
"
S
"
sum
To Press ÉTO
" .
↳ Press A
] In
blue
t= after a term
↳ Clear
r= @ interest rate p a -
"
.
"
> Known as PV of sum S
4) Calculate
.
:
↳ 5- Prt "
PV of
"
" • The a debt S @ date
5=50004+0115 ✗ fraction saved!
a
prior to the due date is the
↳ Press RCL
" " "
A
"
& "
"
P PV
" "
value or of the debt
5184193
=
@ the date in
question .
,Exercise 2.2
5
F- are
12000
=
← work this out first
ltrt
to =
1+0,12×2
424
=
12000
=
I 24
2.2. Timelines
•
Represent interest rate calculations
Time flow
•
presented by horizontal line
-
.
arrow from above
• Inflows indicated
by pointing to line
-
.
Outflows indicated downward below timeline
by
• -
arrow .
Simple interest timeline
Present
value
¢
-
Py E- term .
F- interest rate Future value
5=171+1 t )-
PV
Beginning of term
=
FV= Amount accumulated / receive @ end of term .
NOTE ↓
* Sum accumulated includes the interest .
'
. . 5 =P + Prt
= Pcitrt)
* FV = PV + Interest .
±
Exercise 2.1 Timeline Exercise 2.2 Timeline 1
5000 90 9677142
± ¢ ¥ a
I
F- 15 %
¥5184,93 r -72 %
12000
Value was known we asked to find the PV .
,2.3. Simple Discount
Interest calculated FV
Formula
'
on the
of a term & paid @ the
beginning
,,,,,,,,g,
of the term = DISCOUNT
D= Sdt
paid @ beginning /
< Interest can be
D= Discount
end of term
5 FU
.
=
T> lender deducts the interest from
principal in advance .
D= Discount rate
^ Time
/
to =
term
→ @ the end of term
only the
a
principal is due .
. . D= S D -
- Amount advanced tender discount
by =
=
5- Sdt
to The PV of paid
to be back
SCI dt )
sum
= -
using the PV technique .
Ep Given "
S
"
& asked to calculate
"
P
"
.
OR
a
t
i
> PV=FV FVX discount -
rate ✗ Time
= FU - ( FV ✗ d ✗ E)
a
↑
5
"
- Discount on sum
"
S
Tp Difference between FV & PV
✓
" "
Discount d
given by
- :
D= S P
Expressed
-
in timeline
Example 2.1.
v
PV= Present value /
discounted value
at
g- Term of discount -1> Discount
A- rate
↑
Future
"
value S
"
- Similar to simple interest
timeline .
-
Simple discount -
-
expressed as %
of FU
Tp
"
"
'
n
sign in formula
-
means discount
①
.
✗dxt
-
-
subtracted from FV=PV .
{ NOTE :
Interest rate & discount rate not the same
-_
↑ ↑
Acts on PV Acts on FV
, 2.3. Simple Discount
Exercise 2.3.1
[
f- R4000
D= 0118
E- E- / E
D= Sdt
=
4000×0/18 ✗ É
=
R360 is the discount
The discount value is :
F- S D -
=
4000 -
360
=
123640 you will receive .
Since interest paid is 12360 :
I =
Prt
360=3640 ✗ r ✗ É
= 360
3640 =
r ✗
£
=
360 2
3640 ✗ 1- =
r
360
=
r= 3640×2
=
0,1978
i.
equivalent simple interest -19.78% p.a.
-
, Chapter 2 Simple interest & Simple discount
a
2.1. Simple interest
Interest price paid for the use of borrowed
money
• = .
who lender
Party borrows
pays interest to
-
•
- .
• Interest -
Calculated as a friction of the amount borrowed .
Friction Interest rate Expressed as % (0112--124)
per year
• = - .
•
simple interest :
calculated on principal amount borrowed .
Example
Simple in thrust is
computed on the
D principal for the entire
term of the loan &
is due @ the end of
term .
Formula
I. Prt
F- Interest paid @ end of term .
F- Principal
F-
/ total
Rate of interest
amount
.
borrowed
/ PV of loan .
b- =
Time in YEARS .
Interest rate per annum, then the term must be in
years
• =
or fraction thereof .
-
. .
We need to
change the months days or weeks to fraction
,
a
the months by the number of
of a
year by dividingCIZ) & weeks ÷ 52 &
months in a
year , ,
days ÷ 365 .
,2.1. Simple interest
The accumulated G)
Maturity
•
sum =
value
=
Future value
=
Accused principal .
@ end
" "
of term t is
given by :
5- Pcitrt )
5- Principal value + interest
5 =
PTI
s =
Pt Prt
Pcitrt)
≤ Date @ the end of term
5 =
@ which the debt is to
↳ law of multiplication over addition .
be
date
paid
.
= due date
/ maturity
i. abtac = a Cbtc )
q =P < .
b- I-
- . Plt Prt = Part )
[ =
rt
←
Exercise 2.1
5- Patris)
-
← Can turn basic formula
"
I =
Prt
"
inside
=
50004+1%0 ✗¥5 ) out .
The concept of PV is obtained
=
5000 (11-0,15×5%5) 4- enter as is on calc .
by basic formula for the sum of FV
"
S
"
= 125184,93 .
: 5- Pcltrt )
( Hrt ) gives :
Calculator dividing by factor
1) Setup 0 Do a Decimal
- - =
P=¥rt
2) Divide time by fraction
.
Save fraction
3) f- Amount that must be borrowed
To 90.1-365 ^
to accrue the
"
S
"
sum
To Press ÉTO
" .
↳ Press A
] In
blue
t= after a term
↳ Clear
r= @ interest rate p a -
"
.
"
> Known as PV of sum S
4) Calculate
.
:
↳ 5- Prt "
PV of
"
" • The a debt S @ date
5=50004+0115 ✗ fraction saved!
a
prior to the due date is the
↳ Press RCL
" " "
A
"
& "
"
P PV
" "
value or of the debt
5184193
=
@ the date in
question .
,Exercise 2.2
5
F- are
12000
=
← work this out first
ltrt
to =
1+0,12×2
424
=
12000
=
I 24
2.2. Timelines
•
Represent interest rate calculations
Time flow
•
presented by horizontal line
-
.
arrow from above
• Inflows indicated
by pointing to line
-
.
Outflows indicated downward below timeline
by
• -
arrow .
Simple interest timeline
Present
value
¢
-
Py E- term .
F- interest rate Future value
5=171+1 t )-
PV
Beginning of term
=
FV= Amount accumulated / receive @ end of term .
NOTE ↓
* Sum accumulated includes the interest .
'
. . 5 =P + Prt
= Pcitrt)
* FV = PV + Interest .
±
Exercise 2.1 Timeline Exercise 2.2 Timeline 1
5000 90 9677142
± ¢ ¥ a
I
F- 15 %
¥5184,93 r -72 %
12000
Value was known we asked to find the PV .
,2.3. Simple Discount
Interest calculated FV
Formula
'
on the
of a term & paid @ the
beginning
,,,,,,,,g,
of the term = DISCOUNT
D= Sdt
paid @ beginning /
< Interest can be
D= Discount
end of term
5 FU
.
=
T> lender deducts the interest from
principal in advance .
D= Discount rate
^ Time
/
to =
term
→ @ the end of term
only the
a
principal is due .
. . D= S D -
- Amount advanced tender discount
by =
=
5- Sdt
to The PV of paid
to be back
SCI dt )
sum
= -
using the PV technique .
Ep Given "
S
"
& asked to calculate
"
P
"
.
OR
a
t
i
> PV=FV FVX discount -
rate ✗ Time
= FU - ( FV ✗ d ✗ E)
a
↑
5
"
- Discount on sum
"
S
Tp Difference between FV & PV
✓
" "
Discount d
given by
- :
D= S P
Expressed
-
in timeline
Example 2.1.
v
PV= Present value /
discounted value
at
g- Term of discount -1> Discount
A- rate
↑
Future
"
value S
"
- Similar to simple interest
timeline .
-
Simple discount -
-
expressed as %
of FU
Tp
"
"
'
n
sign in formula
-
means discount
①
.
✗dxt
-
-
subtracted from FV=PV .
{ NOTE :
Interest rate & discount rate not the same
-_
↑ ↑
Acts on PV Acts on FV
, 2.3. Simple Discount
Exercise 2.3.1
[
f- R4000
D= 0118
E- E- / E
D= Sdt
=
4000×0/18 ✗ É
=
R360 is the discount
The discount value is :
F- S D -
=
4000 -
360
=
123640 you will receive .
Since interest paid is 12360 :
I =
Prt
360=3640 ✗ r ✗ É
= 360
3640 =
r ✗
£
=
360 2
3640 ✗ 1- =
r
360
=
r= 3640×2
=
0,1978
i.
equivalent simple interest -19.78% p.a.
-
