Bonus Problem 2 (Optional, 25 marks) An investment fund (Fund A) has been launched at time 0. It is given that the fund earns interest at a force of interest 8t = max{0.01, 0.02t2 – 0.08t + 0.07}, where t > 0. It is given that the annual inflation rates over 1st year, 2nd year, 3rd year, 4th year and 5th year are 1%, 1.6%, 2%, 1.5% and 1.7% respectively.

(a) Calculate the real rate of interest of the investment fund over the period [1,4].
(b) An investor deposits $1600 in the investment fund at time 0. After that, the investor deposits $2000 and $1500 at time 1.5, 3.5 respectively. In addition, the investor has withdrawal an amount $1000 at time 2. Calculate the total amount of interest earned by the investor over the period (1,3] (i.e. 2nd year plus 3rd year)

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