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 account II has force of interest equal to : 0.04/(1+0.05t^(2))
Investment account III is governed by the accumulation function: aIII(t)= 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.
I know that I have to compare first delta t values and any given time compare whichever account providing greatest return in given time use that account for that t however I suppose my calculations for delta t values slightly off.
delta t account 1 = -ln(1-d) delta t account 2 given delta t account 3= a`(t)/a(t) which gives function 2t/(200-t^2)
using this values I obtained above answer which is very wrong. Would you point me out where am I doing wrong. Thanks