QUESTION 5 An individual is thinking about investing in a fund with annual interest earned is a collection of i.i.d random variables with mean 0.05 and standard deviation 0.02. He wants to make a single deposit of $800 to be accumulated for 5 years under the stochastic interest rate model. (a) Calculate the expected value of the accumulation. [1 mark] (b) Calculate the standard deviation of the accumulation. [3 marks) (C) After careful analysis, the individual decided instead to do a deposit of $100 at the beginning of each year for 3 years only and a single deposit of $200 at the end of the 4th year, [2 mks) i) Draw a timeline to represent the information above (ii) Calculate the Expected value of the accumulation at the end of year 5. [4 mks) Hint: Treat the single deposit and the annuity separate (iii) Standard deviation of the accumulation at the end of the 3rd year. (5 mks) QUESTION 5 An individual is thinking about investing in a fund with annual interest earned is a collection of i.i.d random variables with mean 0.05 and standard deviation 0.02. He wants to make a single deposit of $800 to be accumulated for 5 years under the stochastic interest rate model. (a) Calculate the expected value of the accumulation. [1 mark] (b) Calculate the standard deviation of the accumulation. [3 marks) (C) After careful analysis, the individual decided instead to do a deposit of $100 at the beginning of each year for 3 years only and a single deposit of $200 at the end of the 4th year, [2 mks) i) Draw a timeline to represent the information above (ii) Calculate the Expected value of the accumulation at the end of year 5. [4 mks) Hint: Treat the single deposit and the annuity separate (iii) Standard deviation of the accumulation at the end of the 3rd year. (5 mks)