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 . Investment account III is governed by the accumulation function a^III(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?

the answer is 12140.26

.04 1 +.05t2