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Homework IV: June 30, 2009
1.79. Let m be a positive integer, and let m be the integer obtained from m by reversing its (decimal) digits. Prove that m m is a multiple of 9. Let a = dk d1 d0 , where the di are the decimal digits of a positive integer a.
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Homework III: June 26, 2009
1.78(iii). Find all the integers s which are solutions to the congruence 243x + 1 101 mod 725.
The Euclidean Algorithm gives 1 = 18224361725. Hence, 243x+17 101 mod 725 gives 23x 84 mod 725, and x 182 84 = 15288 63 mod 725. T
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Homework II: June 23, 2009
1.58. Prove that if gcd(r, m) = 1 = gcd(r , m), then gcd(rr , m) = 1. Since gcd(r, m) = 1, there are integers s, t with 1 = sr+tm; since gcd(r , m) = 1, there are integers s , t with 1 = s r + t m. Multiplying, 1 = (sr + tm)(s
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Homework I: June 19, 2009
1.9. Find a formula for 1 + is correct.
n j =1
j !j ; use induction to prove that your formula
A list of the sums for n = 1, 2, 3, 4, 5 is 2, 6, 24, 120, 720. These are factorials; n better, they are 2!, 3!, 4!, 5!, 6!. If we w
Last Assignment
( There are 4 problems due: Thursday, April 28 )
1.
Titan Mining Corporation has 15 million shares of common stock
outstanding, and 200,000 of 8.4 percent semi-annual coupon, $ 1,000 par
value bonds outstanding. The common stock currently
Assignment 4
( There are five problems due: Thursday, April 14 )
1.
Suppose the expected returns and standard deviations of stocks A, B, and
C are as follows
E(RA) = 0.15, E(RB) = 0.25, E(RC) = 0.30, A = 0.40, B = 0.5, C = 0.6.
Assume that correlation (A
Team Assignment 3
( due : Thursday, March 4 )
1.
The annual earnings of XYZ Inc., will be $ 5 per share for the next three
years after which it will be $ 6 per share in perpetuity if the firm makes no
new investments. Under such a situation the firm would
Team Assignment 2
( due: Tuesday, February 22 )
1.
Consider a bond that has a coupon rate of 10 % per year, with the coupons being
paid semiannually. The yield to maturity is 8 %. The bond has 7 years until
maturity and has a par value of $ 1,000.
(a)
Fin
Team Assignment 1 ( due: Tuesday, February 8 )
1.
You have just won the lottery. You will receive $ 3,500,000 today, and then receive 36 payments
of $ 800,000. These payments will start one year from now and will be paid every four months.
A representativ