3. Assume that the interest rate rt follows drt=a(brt)dt+crtdBt, where a,b,c>0. Solve for rt by the following steps. (a) Write St=exp((a2c2)t+cBt). Derive the SDE for St1. (b) Show that d(rtSt1)=abSt1dt. (c) Hence find the explicit representation of rt. [Remark: This is just a special case of the general procedure given in the lecture note: (1) solve the SDE only involving rt:dSt=aStdt+cStdBt, (2) let rt=StZt, and then derive a SDE for Zt ] 3. Assume that the interest rate rt follows drt=a(brt)dt+crtdBt, where a,b,c>0. Solve for rt by the following steps. (a) Write St=exp((a2c2)t+cBt). Derive the SDE for St1. (b) Show that d(rtSt1)=abSt1dt. (c) Hence find the explicit representation of rt. [Remark: This is just a special case of the general procedure given in the lecture note: (1) solve the SDE only involving rt:dSt=aStdt+cStdBt, (2) let rt=StZt, and then derive a SDE for Zt ]