4. FORWARD DISCOUNT FACTORS, SPOT RATES AND PRESENT VALUE Suppose that the spot rates St = 3% for t 10 years (continuously componded), i.e. all forward rates starting from 10 years are 5%. (a) For t > 10 years, what is the forward discount factor d10,t? (Hint: Use the forward rate) (b) Using part (a), for t > 10 years, what is the discount factor dt? 1 2 JOHN C. MILLER (c) By combining the 10 year spot rate and the forward rate f10,4 = 5%, for what is the spot rate for t > 10 years? (d) Suppose that you receive $1 million starting at year 11 and continuing annually in perpetuity. What is the present value of this? (Hint: Use discount factors calculated in part (b). 4. FORWARD DISCOUNT FACTORS, SPOT RATES AND PRESENT VALUE Suppose that the spot rates St = 3% for t 10 years (continuously componded), i.e. all forward rates starting from 10 years are 5%. (a) For t > 10 years, what is the forward discount factor d10,t? (Hint: Use the forward rate) (b) Using part (a), for t > 10 years, what is the discount factor dt? 1 2 JOHN C. MILLER (c) By combining the 10 year spot rate and the forward rate f10,4 = 5%, for what is the spot rate for t > 10 years? (d) Suppose that you receive $1 million starting at year 11 and continuing annually in perpetuity. What is the present value of this? (Hint: Use discount factors calculated in part (b)