financial mathematics sd
TRANSCRIPT
7/25/2019 Financial Mathematics SD
http://slidepdf.com/reader/full/financial-mathematics-sd 1/6
FINANCIAL MATHEMATICS
I. Commission: When we change currency in an exchange shop or in a bank
they usually charge a fee called “commission” for the service, which is at a
percentage rate of the total amount
Example:
(a) 1.7700
(b) 2% of 1000 CHF = 20 CHF
So he will change 1000-20 = 980 CHF
Jin is travelling from Korea to Japan. The
bank sells
1 Korean Won(KRW) = 0.1219 Japanese Yen
Jin pays 1 million KRW.
How much does she receive in JPY if a
commission is charged at a rate 2%?
The bank will keep 2% of 1 million KRW
So:
21000000 20000
100
KRW
Therefore Jin changes
1000000-20000=980000 KRW to JPY
→ 980000 0.1219 = 119462 JPY
7/25/2019 Financial Mathematics SD
http://slidepdf.com/reader/full/financial-mathematics-sd 2/6
1 USD → 1.7700 CHF
x → 980 CHF
980553.67 $554
1.7700 x
(a) 100 INR → S$3.684
x → S$500
100 50013572 INR
3.684 x
(b) The commission is3
2500 75 Indian rupees100
So she is going to change 2500-75=2425
Indian rupees
100 INR → S$3.672
2425 INR → x
2425 3.672$89.05
100 x S
7/25/2019 Financial Mathematics SD
http://slidepdf.com/reader/full/financial-mathematics-sd 3/6
II. Simple Interest: Interest is most commonly the price paid for the use of
borrowed money or money earned by deposited funds. Capital is the money
invested in a bank or savings institution. The simplest relation between interest
and capital is called simple interest.
I100
I : Interest
: Capital
r: %rate
n: number of time periods
Crn
C
Example:
Calculate the time needed for a capital amount of 4000 EUR to double if invested at a simple
interest rate of 5%
The capital C is 4000 EUR and this has to become 8000.
Hence the interest I=8000-4000=4000 EUR
I100
4000 54000
100
4000 100 20000
400000 20000
20 years
Crn
n
n
n
n
7/25/2019 Financial Mathematics SD
http://slidepdf.com/reader/full/financial-mathematics-sd 4/6
III. Compound Interest: Compound interest arises when interest is added to
the principal, so that from that moment on, the interest that has been added
also itself earns interest. This addition of interest to the principal is called
compounding .
In a simplest way, now the interest is calculated as a percentage of the
new capital amount through each period which seems to be more fair to theinvestor.
T (1 )100
Interest I (1 )100
I : Interest
: Capital
r: %rate
n: number of years
k: number of time periods e.g yearly: k=1
monthly: k=12
kn
kn
r Total amount C
k
r C C
k
C
quarterly: k=4
half-yearly: k=2
28
10000 5 28( ) I= 14000 (Simple Interest)
100
5(b) I=10000(1+ ) 10000 29201.29 (Compound Interest)
100
a CHF
CHF
7/25/2019 Financial Mathematics SD
http://slidepdf.com/reader/full/financial-mathematics-sd 5/6
12
1
12
( ) Choice A: 100x12=$1200
12 Choice B: 1100(1+ ) =$1239.51
100 12
Choice C: 75+80+...=arithmetic sequence with u 75 and d=5
12 S (2 75 (12 1) 5) $1230
2
Choice D: 80+8
a
21
12
12
0 1.05+80 1.05 +...=geometric sequence with u 80 and r=1.05
(1.05 1) S 80 $1273.37
1.05 1
2
( ) Choice D because the total amount is higher
(c) 1452=1200(1+ )100
r=10%
b
r
7/25/2019 Financial Mathematics SD
http://slidepdf.com/reader/full/financial-mathematics-sd 6/6
IV. Inflation: In economics, inflation is a rise in the general level of prices of
goods and services in an economy over a period of time. When the general price
level rises, each unit of currency buys fewer goods and services. Consequently,
inflation also reflects an erosion in the purchasing power of money – a loss of
real value in the internal medium of exchange and unit of account in the
economy. A chief measure of price inflation is the inflation rate, the annualizedpercentage change in a general price index over time.
In order to make calculations concerning inflation we use the compound
interest formula for k=1 (yearly)
T (1 )
100 T new price
old price
inflation rate
years
nr C
C
r
n
3
2
2
4.5( ) 1.70(1 ) $1.94
100
4.5( ) 40000 (1 )
100
40000 $37000 ( correct to the nearest thousand dollars)
4.5(1 )100
a T
b C
C answer