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 acount II has force of interest equal to {.04}/{1+.05t^{2}} . Investment account III is governed by the accumulation function aIII(t) = (1 - .005t2)^-1. 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, begin by determining te 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 to accumulation functions for the accounts in order to determine Mr. Valdez's balance at t = 5. ]