Nick has lost faith in the banks, and has decided to diversify his portfolio by keeping some money under his mattress. He decides to put $2500 under his mattress and$2500 in a GIC with a 11% annual interest rate (compounded continuously). If there is a 6% annual inflation rate, when will the real value of Nick's investments be at a minimum?

NOTE: An inflation rate of 6% means that the real value of money is decreasing at this rate (compounded continuously). You should also consider what inflation does to the interest rate.

If $I(t)$ is the total real value of the investments after $t$ years:
$I(t) =$

If $t^*$ is the number of years until the value of the assets is a minimum:
$t^* =$