Mr. Valdez has \$$10000$ 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 $$\dfrac{0.04}{1+0.05t^{2}}.$$ Investment account III is governed by the accumulation function $$aIII(t) = \frac{1}{(1 - 0.005t^2)}.$$ 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 correct answer is $12140.26$ dollars, but the highest investment I got was $11643.4772$ dollars.