INVESTMENT RETURN MODEL

1. Annual rates of return on an investment fund are assumed to be independent and identically distributed. Each year the distribution of 1+i is lognormal with parameters = 0.20 and ^2 = 0.01 , where i is the annual yield on the fund. Show with workings what is the amount that should be invested in the fund immediately to ensure an accumulated value of at least $100,000 in 5 years' time with a probability of 0.99. Ans: $61,889.92
2. Annual return on a fund, i are independent and identically distributed. Each year, distribution of 1+i is lognormal with parameters = 0.02 and ^2 = 0.3^2 . What are the upper and lower quartiles for the accumulated value at the end of 3 years of an initial investment of $1,000. Ans: Lower quartiles = 747.91, upper quartiles = 1,507.53

• The answers are as given after each question. What are the proper workings for these two questions ??