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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 πΌππππ₯ πππ πππ¦ππ = Household ππ π0 π₯100 π0 π0 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 π =π 1+ 100 ο P = principal ο S = future value ο r = interest rate ο t = time π Find the value , in 10 years time, of $1000 invested at 8% interest compound annually! Solution: 10 8 π = 1000 1 + 100 π = 1000 1.08 10 π = 1000 2.158 π = $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?