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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?