Exam (elaborations)
APS502 Financial Engineering Midterm
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Exam of 2 pages for the course APS502 at U of T (N/A)
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APS 502 Financial Engineering 1 Winter2015, March 12
Instructions: Closed book and closed notes except for one side of a 3 by 5 inch
notecard. Only a simple scientific non-financial calculator with no programming
capability is allowed. Please write neatly as this will aid in providing maximum
partial credit. IMPORTANT: Interpretation of the exam questions is
part of the exam and so no questions will be taken that ask for clar-
ification of the question. You must turn in this question sheet with
your answer booklet or else your exam will NOT be marked.
Problem 1 (18 points, 6 points each)
Mom4.7560 0.0475
An internet company i-Money is o§ering a savings account with a nominal
annual interest rate of 4.75%. What is the e§ective annual interest rate o§ered
by i-Money if the compounding is
AI
(a) Annual
(b) Monthly 475
485 m.ir kff CHM ommjm
1 4.8651
f soooo
(c) Continuously
3500 1526500
Simo
Problem 2 (15 points)
You are considering buying a car whose price is $30,000. The car salesman,
At who is eager to sell the car, o§ers you an attractive financing (loan) package:
you need to make a down payment of $3,500 and pay the rest over 5 years in A 1.0215 I
A5 equal annual payments at an annual interest rate of 2%. The o§ered interest
rate of 2% is not necessarily the market interest rate.
(a) (7 points) What is the annual payment to the care salesman?
0.02 f 21 5622.20
4 42590 (b) (8 points) The car salesman o§ers you a second option: you pay cash
for the car, but get a $2,500 rebate. Which is better for you getting the loan or ebateopfion
1 95.92
paying cash? Assume the market annual interest rate is constant at 5%. 2500
t.gg p 3oooo
a Problem 3 (18 points, 6 points each)
4259 Suppose you are given the following information about three zero coupon HO
5 bonds:
Bond Maturity Price firstoption
OO
92.01 A 1 95.92
ftp SE
B
C
2
3
92.01
87.00
(a) Compute the implied spot rates s1 , s2 , s3
ftp.ffy g.pt
KO 87475
(b) Compute the implied forward rate between years 2 and 3 i.e. f2,3 . 13500
Ftl
(c) Compute the yield of a 2 year bond with coupon rate of 4.25% and annual
coupon payments. The face value of the bond is $100. 27841.18
Problem 4 (24 points, 8 points each)
b
You have an obligation (liability) of $1 million per year for the next 20 years
(a liability payment is due at the end of each year), and you wish to invest now
should i You pay
cash
I I
to meet that obligation. You can invest in the following two zero coupon bonds:
Bond A
maturity
5 years
r ao4 liability floooooo 1000000
5.76 Year I 20
Bond B 20 years
Since 5 52
1
A 0.04
c A 4.25
Pliability
9511 4
t 110
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a 1.04110
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