Find an expression of t in terms of 8 so that f(t)= (1 + it) -...

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Find an expression of t in terms of 8 so that f(t)= (1 + it) - (1 + i)' is maximum. [5 marks] b. An investor invests $1,000 into an investment account at time 1. The interest is computed based on the following force of interest: (0.02t &=0.025 0 (i) (ii) 0 ≤t<3 3 St otherwise Find the amount of interest generated between time 2.5 and 3.5. Calculate the effective discount rate during the third period, i.e., d3. [8+3=11 marks] c. Investor A deposits $10,000 into an account paying 2% compounded quarterly. At the end of six years, he deposits an additional 10,000. Investor B deposits X into an account with force of interest d = After ten years, investors A and B have the same 3+t amount of money. Find X. Find an expression of t in terms of 8 so that f(t)= (1 + it) - (1 + i)' is maximum. [5 marks] b. An investor invests $1,000 into an investment account at time 1. The interest is computed based on the following force of interest: (0.02t &=0.025 0 (i) (ii) 0 ≤t<3 3 St otherwise Find the amount of interest generated between time 2.5 and 3.5. Calculate the effective discount rate during the third period, i.e., d3. [8+3=11 marks] c. Investor A deposits $10,000 into an account paying 2% compounded quarterly. At the end of six years, he deposits an additional 10,000. Investor B deposits X into an account with force of interest d = After ten years, investors A and B have the same 3+t amount of money. Find X.