Stony Brook University Financial Mathematics Problem Solving Exercise Fully explain your thought process for the above problem and clearly state your answe

Stony Brook University Financial Mathematics Problem Solving Exercise 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. .04
17.0512
(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 Investment account III is governed by the accumulation function
a””(t) = (1 – .00502)-!. 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).)

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