Please answer the following questions, show full calculations, explanations and proofs:

1. Bond pricing In class, we have discussed the pricing of bonds with finite maturity, deriving the bond formula Here, B is the current bond price, T is the number of periods to maturity, r> 0 is the per-period discount rate, C is the compon, payment, and P is the principal payment due at maturity. A variation of the bond is a perpetuity, which perpetually makes per-period coupon nayments and thus never mitte. It follows that the price of the perpetuity is B- (a) Consider a growing perpetuity, that makes the payment after one period, C(1 +9) after two periods, C(1+919 after three periods, etc., where 0