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Mathematics for Finance
Dr. Ananda Sabil Hussein
Math For Finance
ο‚— Index number = scale factor from base year X 100
ο‚— 𝐼𝑛𝑑𝑒π‘₯ π‘™π‘Žπ‘ π‘π‘’π‘¦π‘Ÿπ‘’ =
Household
𝑃𝑛 𝑄0
π‘₯100
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 =
π‘₯100 = 103.8
Index number of 2000 =
697.2
716.6
π‘₯100
697.2
= 102.8
Interest Rate and
Investment Appraisal
π‘Ÿ
𝑆 =𝑃 1+
100
ο‚— P = principal
ο‚— S = future value
ο‚— r = interest rate
ο‚— 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
ο‚— 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
ο‚— 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?