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MACT4012 Notes
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This note covers Chapter 1 to Chapter 14 and Chapter 18. A simplified version of lecture notes with all the important formulas highlighted in Purple boxes.
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,CH1 :NOMINAL INTEREST RATE
Effective Interest Rates
1. Effective i rate :
interest compounds from year to
year
Def the amount of i of I at the end of
T
.
2 : earn ,
expressed as a
proponic of initial amount
.
3 Example :
12 % per annum = i per month =
E :
1%
Nominal Interest Rates
Nominal expressed but paid
1 . i rale =
annally , monthly (ACE)
.
2 Have to change to effective
: .
per month
I %12 .
60 %
Nominal of time defined of transaction of term
i rate per unit
.
3
number of <P)
↓ or i
time period >
-
p
↳ the effective i rale
:
4
. Norminal i rale unit of line beginning at time +,
per I
on transactions of term h is defined to be in (t)
* the effective race of interest is him (t)
.
5 Annual nominal interest rate
,
convertible monthly
, iP
6
. Nominal rule of interest or in (t) convertible
termly
(a) Effective rate of interest rate i unit of time
, , per
i =
((1 +
1) 1] -
or i =
(3) +
min(t)) -
1)
16 1 We also these to in
can rearrange equ express
i
(p)
p((Itilt-1] (1 + ish 1
in (e)
-
= or :
h
, CH 2 : FORCE OF INTEREST effective :
per month
total number ↓
X
of month
I -
*
number
of months
i(p)
effective interest rale or him (t)
p
0
h)
=)A(t 1)
+
A(t t
t
(1 (1
+ = +
, + , =
.More
2 and more shorter and shorter Result in an
un-countably
h
intervals ,
length large
> >
intervals
-
-
, p , p
& infinitesimal h
length
shrinking
,
h p >
-
infinity
Force of interest 8 amount of interest paid continuously
.
3 >
-
over a unit of time
4
. Formulae of 8 as a function of time
& (t) =
yo +
un(t) 8 =
piP
.
5
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