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 $4500 under his mattress and $4000 in a GIC with a 12% annual interest rate (compounded continuously). If there is a 8% annual inflation rate, when will the real value of Nick's investments be at a minimum? NOTE: An inflation rate of 8% 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.
1. If I(t) is the total real value of the investments after t years: I(t)=
2. If t∗ is the number of years until the value of the assets is a minimum: t∗=