3. Derive the growing perpetuity formula. (Hint: this is very similar to what we did in class. Write out the PV of the (infinite) sum of discounted cash flows and multiply both sides by 1+g Suppose you extend a loan to a friend this year for $1000 in exchange for repayment next year of $1100 (the $1100 is the principal plus interest). Every year, however, the friend has the option to borrow $1000 again in exchange for $1100 repayment one year later, i.e. the friend can roll over the debt. You know this friend well and know that he will always roll over the debt and will never default. 4. Assume neither of you will ever die. What is the NPV of this infinite stream of loans if you have a discount rate of 8%? Now assume your friend today is t-0 and your friend will die immediately after paying back his loan at t-60. What is the NPV of this finite stream of loans if you have a discount rate of 8%? a. b