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
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
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
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.
(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?