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```Mathematics for Finance
Dr. Ananda Sabil Hussein
Math For Finance
 Index number = scale factor from base year X 100
 𝐼𝑛𝑑𝑒𝑥 𝑙𝑎𝑠𝑝𝑒𝑦𝑟𝑒 =
Household
𝑃𝑛 𝑄0
𝑥100
𝑃0 𝑄0
1997
1998
1999
2000
2001
686.9
697.2
723.7
716.6
734.5
spending
A base year is chosen and the value of 100 is allocated to that year. I
f we choose 1998 as the base year then the index number of 1998 is 100.
Calculate the index number of 1999 and 2000 !
Solution:
723.7
Index number of 1999 =
𝑥100 = 103.8
Index number of 2000 =
697.2
716.6
𝑥100
697.2
= 102.8
Interest Rate and
Investment Appraisal
𝑟
𝑆 =𝑃 1+
100
 P = principal
 S = future value
 r = interest rate
 t = time
𝑛
Find the value , in 10 years time, of \$1000
invested at 8% interest compound annually!
Solution:
10
8
𝑆 = 1000 1 +
100
𝑆 = 1000 1.08 10
𝑆 = 1000 2.158
𝑆 = \$2158
Question
 This table shows the number of items (in thousands)
produced from a factory production line during the
course of a year. Taking the second quarter as the
base quarter, calculate the associated index
numbers.
Output
Q1
Q2
Q3
Q4
13.5
1.4
2.5
10.5
Practice
 You are given the opportunity of investing in one of
the three projects. Projects A, B and C require initial
outlays of \$20000, \$30000 and \$100000 and are
guaranteed to return \$25000, \$37000 and \$117000
respectively in three years time. Which of these
projects would you invest in if the market rate is 5%
compounded annually?
```
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