Fully explain your thought process for the above problem and clearly state your answer(s). Please include one graph of delta-t versus t for all 3 investments as part of your justification and make sure you are answering ALL the questions asked in this problem to earn full credit Hint: Draw the graph of delta-t versus t and then examine it carefully to determine the intervals where each curve prevails. Then use the corresponding a(t) for that prevailing curve to accumulate in that time interval. Ex. if (II) is the highest curve from 0 to t1, then the accumulated value at t1 is a(t1). We discuss this kind of situation in the notes Lecture 1B, class notes page 4G, 4H. Total 5 points. 1 point for correct delta-t for investment 1 point for alt) for investment II 1 point for correct delta-t for investment III 1 point for the correct values oft 1 point for correct final answer .04 (10) Mr. Valdez has $10,000 to invest at time t = 0, and three ways to invest it. Investment account I is governed by compound interest with an annual effective discount rate of 3%. Investment account II has force of interest equal to 1+.0512 Investment account III is governed by the accumulation function q"(t) = (1 - .005t2-. Mr. Valdez can transfer his money between the three investments at any time. What is the maximum amount he can accumulate at time t = 5? [HINT: At all times, Mr. Valdez wishes to have his money in the account that has the greatest force of interest at that moment. Therefore, be- gin by determining the force of interest function for each of the investment accounts. Next decide for which time interval Mr. Valdez should have his money in each of the accounts. Assume that he accordingly moves his money to maximize his return. You will then need the accumulation functions for the accounts in order to determine Mr. Valdez's balance at t = 5. Remember to use Important Fact (1.7.4).] Fully explain your thought process for the above problem and clearly state your answer(s). Please include one graph of delta-t versus t for all 3 investments as part of your justification and make sure you are answering ALL the questions asked in this problem to earn full credit Hint: Draw the graph of delta-t versus t and then examine it carefully to determine the intervals where each curve prevails. Then use the corresponding a(t) for that prevailing curve to accumulate in that time interval. Ex. if (II) is the highest curve from 0 to t1, then the accumulated value at t1 is a(t1). We discuss this kind of situation in the notes Lecture 1B, class notes page 4G, 4H. Total 5 points. 1 point for correct delta-t for investment 1 point for alt) for investment II 1 point for correct delta-t for investment III 1 point for the correct values oft 1 point for correct final answer .04 (10) Mr. Valdez has $10,000 to invest at time t = 0, and three ways to invest it. Investment account I is governed by compound interest with an annual effective discount rate of 3%. Investment account II has force of interest equal to 1+.0512 Investment account III is governed by the accumulation function q"(t) = (1 - .005t2-. Mr. Valdez can transfer his money between the three investments at any time. What is the maximum amount he can accumulate at time t = 5? [HINT: At all times, Mr. Valdez wishes to have his money in the account that has the greatest force of interest at that moment. Therefore, be- gin by determining the force of interest function for each of the investment accounts. Next decide for which time interval Mr. Valdez should have his money in each of the accounts. Assume that he accordingly moves his money to maximize his return. You will then need the accumulation functions for the accounts in order to determine Mr. Valdez's balance at t = 5. Remember to use Important Fact (1.7.4).]