# Midterm winter 2023

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APS 502 Financial Engineering I March. 2, 2023 Instructions: Closed book and closed notes except for one side of a 3 by 5 inch notecard. Only a simple scienti°c non-°nancial calculator with no programming capability is allowed. Please write neatly as this will aid in providing maximum partial credit. Show All Work. IMPORTANT: Interpretation of the exam questions is part of the exam and so no questions will be taken DURING the exam that ask for clari°cation of the question. You MUST turn in this ques- tion sheet with your answer booklet or else your exam will NOT be marked. Problem 1 (21 points, 7 points each) Suppose that you lend a client \$500,000 and the client will pay you back over the next 30 years using equal monthly payments. Interest will be compounded monthly with a nominal rate of 8.5%. (a) What is the e/ective annual rate on this loan? (b) What is the monthly payment? (c) How much does the client owe you immediately after the 60th monthly payment? Problem 2 (24 points, 8 points each) Suppose you have the following three bonds. Assume all coupon payments are annual and that the face value for all bonds is \$100. Bond Maturity (years) Yield Coupon rate 1 1 4% 4% 2 2 4.2% 5% 3 3 4.8% 5% (a) Determine the price of each bond. (b) Determine the 1 year, 2 year, and 3 year spot rates. (Hint: The price of each bond that you computed in (a) is also equal to the present value of the cash ±ows of the bond where the present value of each cash ±ow is discounted using the appropriate spot rate.) (c) Using the spot rates from (b) and assuming expectation dynamics illus- trate the Invariance Theorem. Problem 3 (24 points, 6 points each) You will be paying \$10,000 a year in tuition expenses at the end of the next two years. Bonds currently yield 6%. (a) What is the present value and duration of your tuition obligation? 1