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principles of risk management

Questions and Answers of Principles Of Risk Management

Given a fair coin, determine the following probabilities:(a) Throwing 2 consecutive heads.(b) Throwing 2 heads and then a tail.(c) Throwing exactly 2 heads in 3 tosses.(d) Throwing at least 2 heads
Given a fair die, determine the following probabilities:(a) Throwing a 3.(b) Throwing a number 3 or larger.(c) In two rolls, throwing a total of 8.(d) In two rolls, throwing a number smaller than 3
Given a normal deck of 52 cards, determine the following probabilities:(a) Drawing the 2 of hearts.(b) Drawing a heart.(c) Drawing a 2 or a heart.(d) Drawing the 2 of hearts in 2 draws (without
Let/(/) = '^v^J Rj denote the denominator of Equation (5.7).7=1(a) Show that V = -4r^. /(O(b) Another concept sometimes encountered is the convexity, f"( '\defined by c = r^J . Show that the
Common stock differs from preferred stock in that the amount of the dividend paid is not constant. In theory, however, the price of a common stock should be equal to the present value of all future
A preferred stock can be thought of as a bond in which the coupons (dividends) continue forever and for which there is no redemption date.(a) Find the price of a preferred stock which pays semiannual
Ten 1000 par-value bonds with semiannual coupons of 50 are issued on January 1, 1992. One bond is redeemed on January 1, 2003, another on January 1, 2004, and so on until the last one is redeemed on
Consider a 100 par-value 15-year bond with semiannual 2%coupons. Assume that this bond is callable at 109 at any coupon date from / = 10 to / = 20 inclusive, at 104.50 from / = 21 to t = 29
In Example 5.13(a), we saw that an investor should pay 885.30 to guarantee himself a return of 6% on the bond described. What yield rate would the investor actually earn if this bond were redeemed at
A 1000 par-value 15-year bond has semiannual coupons of 60 each. This bond is callable at any of the last 10 coupon dates.Find the price an investor should pay to guarantee a semiannual yield rate of
A 10-year par-value bond of 1000 face amount has annual coupons which start at 200 and decrease by 20 each year to a final coupon of 20.(a) Find the price to yield 1 2% per year.(b) Find the yield
A 1000 par-value 10-year bond has semiannual coupons of 6% for the first 5 years and 7% for the last 5 years. Find the price an investor should pay if she wishes to earn (a) 7% per half-year;(b) 14%
Find the price of a 1000 par-value 10-year bond with coupons at 10% convertible semiannually if the buyer wishes a yield rate of(a) 12% per year; (b) 1% per month.AppendixLO1
A 10,000 par-value 20-year bond with semiannual coupons is bought at a premium to yield 12% convertible semiannually. If the amount of principle adjustment in the 18^^ coupon is 36, find the amount
A 1000 par-value 10-year bond with semiannual coupons at 8%convertible semiannually is bought to yield 9% convertible semiannually.Find the total of the interest column in the bond amortization
A 10-year bond of 1000 face amount with semiannual coupons, redeemable at par, is bought at a discount to yield 12% convertible semiannually. If the book value six months before the redemption date
A 5000 par-value bond with semiannual coupons and r = .03 has a yield rate of 5%, convertible semiannually. Find the book value of this bond one year before the redemption date.AppendixLO1
Write a computer program which will construct bond amortization schedules. Test your program on Question 16. If it works, construct the entire bond amortization schedule for Question 1.AppendixLO1
Construct the / = 8 and t = \1 rows of the amortization schedule for the bond given in Question 1.AppendixLO1
Do Question 16 if r = .035 and / = .04.AppendixLO1
Construct a bond amortization schedule for a 3-year bond of 1000 face amount, redeemable at par with semiannual coupons, if r = .035 and /= .025.AppendixLO1
Give a verbal argument for the result shown in Example 5.5.AppendixLO1
For the bond in Question 2, find the book and market values on each of the following dates:(a) June 30, 1999 (1 1:59 p.m.).(b) July 1,2000(12:01 a.m.).(c) March 1,2001.(d) June 23, 2001.AppendixLO1
For the bond in Question 1, find the book value at each of the following times:(a) Just after the 7^^ coupon has been paid.(b) 4 months after the 7^^ coupon has been paid.(c) Just before the S^''
A 6% 100 face value bond with annual coupons, redeemable at the end of n years at 105, sells at 93.04 to yield l\% effective per year. Find the price of a 5% 100 face value bond with annual coupons,
A corporation issues par-value bonds with annual 6% coupons maturing in 5 years, and sells them at a price yielding 4%effective. It is proposed to replace them with 5% bonds having annual coupons.
A 100 par-value bond with semiannual coupons is redeemable at the end of 4 years. At a purchase price of 105.91, the yield rate per half-year is exactly 1% less than the coupon rate per
A 100 par-value 10-year bond with semiannual coupons and r = .035 is selling for 103 . Find the yield rate.AppendixLO1
For a bond of face value \, r = ji and the price is \ -\-p. Find the price of a similar bond with the same number of coupons and the same yield rate, b redeemable at par.but for which r = 4 /. Assume
Two 10-year 100 face value bonds, each redeemable at par, have 8% and 10% semiannual coupons and are priced at^i and A2, respectively, to give the same yield. Prove that the price of a 10-year 1 00
Two 1000 face value bonds, redeemable at par at the end of the same period, are bought to yield 12% convertible semiannually.One bond costs 879.58 and pays coupons at 10% per year convertible
One bond of face value 100 with semiannual coupons and r — .025 costs 15.1A. A similar bond with semiannual coupons and r = .04 costs 1 12.13. Both are redeemable at par in n years and have the
Derive the alternate price formula P^C^(Fr-Ci)a-^. (5.2)AppendixLO1
A 1000 par value bond, with r — .055, has coupons payable on January 1 and July 1, and will be redeemed July 1, 2001. The bond is bought January 1, 1999, to yield 12% convertible semiannually. Find
A 10-year 1000 face value bond, redeemable at par, earns interest at 9% convertible semiannually. Find the price to yield an investor 8% convertible semiannually.AppendixLO1
There are two perpetuities. The first has level payments of/? at the end of each year. The second is increasing such that the payments are q, 2q, 3q, Find the rate of interest which will make the
(a) Show that f.a-^ = -v{Ia)-y(b) Find 4^ a-^ evaluated at / = 0.AppendixLO1
Find the present value at 9% effective of a 20-year annuity, with the first payment due immediately, in which the payments follow the pattern 1, 4, 9, 16, ... , 400.AppendixLO1
Find an expression for the present value of an annuity in which the first payment is due six years from now, and in which the payments follow the pattern n, n—\,n—2, . .., 2, 1,2,
Find the present value at 11% effective of an annuity lasting 20 years in which the first payment of 1,000 is due immediately, and in which each successive payment is 10% more than the payment for
Find the present value of a perpetuity under which a payment of 100 is made after one year, 200 after 2 years, increasing until a payment of 1500 is made, after which payments are level at 1500 per
A loan is repaid by annual payments continuing forever, the first one due one year after the loan is taken out. Assume that the effective rate of interest is /.(a) Find a formula for the amount of
A man borrows money from a bank. He receives the money in 5 annual installments, taking X each time. He repays the loan with 20 annual payments, the first one equal to 100 and the payments increasing
Rank the following in increasing order of magnitude, and give a verbal explanation for your ranking,(a) 3a^ (b)(/a)^ + (Z)«)^ (c) 2(/a)^ (d) loj, (e) 6 AppendixLO1
Redo Question 3-6(a), assuming the annuity is continuous.AppendixLO1
(a) Show that j^S-^ = 1 + (5 -S-y(b) Verbally interpret the result obtained in part (a).AppendixLO1
A fund of 2200 is to be accumulated at the end of 10 years, with payments of 100 at the end of each of the first 5 years and 200 at the end of each of the second 5 years. Find the effective rate of
A fund of 25,000 is to be accumulated at the end of 20 years by annual payments of 500 at the end of each year. Find /.AppendixLO1
Write a general computer program which will solve any problem like Question 51 to any required degree of accuracy.AppendixLO1
Write a computer program which will solve Question 51 by successive approximation. Print out answers which are correct to 3 decimal places, then to 4 decimal places, then to 5 decimal
At what effective monthly rate of interest will payments of 200 at the end of every month for the next 3 years be sufficient to repay a loan of 6500?AppendixLO1
A fund of 5000 is to be accumulated by n annual payments of 50 followed by another n annual payments of 100, plus a final payment, as small as possible, made one year after the last regular payment.
Do Question 47 if the first payment isn't due until two years after the loan is taken out.AppendixLO1
Do Question 47 if the payments are 70 monthly, with the first payment due in one month, and / is still 1 1% per year. Assume the smaller payment is to be made one month after the last regular
Joan takes out a loan of 6000 from her local bank. She wishes to pay it back by means of yearly payments of amount 800 for as long as necessary, with a smaller payment one year later. If the first
A scholarship fund is accumulated by deposits of 400 at the end of each year. The fund is to be used to pay out one annual scholarship of 2000 in perpetuity, with the first scholarship being paid out
Wilbur leaves an inheritance to four charities. A, B, C and D. The total inheritance is a series of level payments at the end of each year forever. During the first 20 years, A, B and C share each
Albert Glover has just signed a contract with the Blue Jays which will pay him 3,000,000 at the beginning of each year for the next five years. To finance his retirement, the player decides to put a
At what effective rate of interest is the present value of a series of payments of 1 at the end of every two years, forever, equal to 10?AppendixLO1
A loan of 5000 is repaid by annual payments continuing forever, the first one due one year after the loan is taken out. If the payments are X, IX, X, IX, . . . and / = .16, find X.AppendixLO1
Deposits of 1000 are placed into a fund at the end of each year for the next 25 years. Five years after the last deposit, annual payments commence and continue forever. If / = .09, find the amount of
A perpetuity of 500 per year, with the first payment due one year hence, is worth 2500. Find /.AppendixLO1
Given / = .15, find the present value of an annuity of 100 per year continuing forever if (a) the first payment is due in one year; (b)the first payment is due immediately; (c) the first payment is
Prove identities (3.14), (3.15) and (3.16).AppendixLO1
An injured worker submits a Workers Compensation claim. It is decided that she is entitled^to annual medical payments of 20,000 a for the next 10 years and equal annual indemnity payments for the
Given d-^ = 9.370 and a—n = 9.499, find the effective rate of interest.AppendixLO1
Given a-^ = \2 and a^;^^ = 21, find ct^y AppendixLO1
A loan of 25,000 is to be repaid by annual payments at the end of each year for the next 20 years. During the first 5 years the payments are k per year; during the second 5 years the payments are 2k
Ifo-^ — X and a^;;-^ — y, express (^as a function of x and>^.AppendixLO1
Derive an expression for the present value of an annuity under which payments are 2, 1,2, 1, . . . at the end of every year for the next 25 years.AppendixLO1
Prove that the accumulated value of the annuity in Question 30 at(\Jr-iY — 1 the time of the last payment is ^^-/^^ . This accumulated value is denoted by s'^K.AppendixLO1
Prove that the present value of an annuity which pays ^ at the end of each m of a year for the next n years is equal to j^ . This present value is denoted by a'^K AppendixLO1
Give verbal interpretations for the formulae in Question 27 and Question 28.AppendixLO1
Show that the accumulated value of the annuity in Question 27 s-i s-\immediately after the last payment is -p AppendixLO1
Consider an annuity where ? payments of 1 are made, the first occurring k years from now with the payments continuing at A:-year intervals thereafter, until a period of n years has passed. Prove
Find the range of interest rates for which each of the contracts in Question 25 has a higher present value then the other two.AppendixLO1
Albert Glover, star third baseman with the Blue Jays, is given a choice of contracts:(a) 3,200,000 per year for the next five years, payable at the end of each year.(b) 3,000,000 per year for the
An annuity consists of « payments of 1, the first to be made at the end of 7 years and the other payments to be made at three year intervals thereafter. Show that the present value of the annuity is
Give a verbal explanation of why the formula in Question 22 is correct.AppendixLO1
A series of « + 1 payments are made as follows: 1 at the end of the first year, 2 at the end of each of the next n — 1 years, and 1 at the end of year n-\- \. Show that the value of these payments
A man wishes to accumulate a small pension by depositing 2500 at the beginning of each year for 25 years. Starting at the end of the year in which the final deposit is made, he will make 20 annual
Rework Question 19 if the nominal rate of interest convertible semiannually is 16% instead of 12%.AppendixLO1
Edward buys a new house and takes out a mortgage of 60,000. To pay off the mortgage, he will make monthly payments with the first payment due in one month. Given p-"^ = .12, find the amount of his
An annuity runs for 25 years as follows: at the end of each of the first ten years 500 is paid, and then at the end of each of the last 15 years 300 is paid. If / = .08, find the value of this
Show that ^(^^ - s-^ = 5^ -^ai' (^+1-^)-AppendixLO1
Give verbal interpretations for the identities in Question 15.AppendixLO1
Prove each of the following identities:(a) a^^^a-^ + X-v"(b) s-^^s-^-X+iX+i)"AppendixLO1
Showthat^ + ^-^ = l.AppendixLO1
Harriet wishes to accumulate 85,000 in a fund at the end of 25 years. If she deposits 1000 in the fund at the end of each of the first 1 years, and 1 000 4- x at the end of each of the last 1 5
Rank n, a-^ and s-^ in increasing order of magnitude. Under what conditions will equality hold for all nl AppendixLO1
Give verbal interpretations for the identities in Question 10.AppendixLO1
Prove each of the following identities:(a) ^ = 1 + ^;r:n(b) ^-^ = ^^TT| - 1 AppendixLO1
Prove that ;|r = ^ + /.AppendixLO1
Give verbal interpretations for each of the identities in Question 7.AppendixLO1
An annuity pays 1000 a year for 8 years. If / = .08, find each of the following:(a) The value of the annuity one year before the first payment.(b) The value of the annuity one year after the last
Alphonse deposits 450 in a bank account at the beginning of each year, starting in 1977 and continuing for 20 years. If/ = .08, find the amount in his account at the end of 1996.AppendixLO1
Answer Question 3 if the loan is to be paid back with 144 monthly payments, the first one due one month after the loan is taken out.AppendixLO1
Henrietta borrows 6500 in order to buy furniture. She wishes to pay the loan back by means of 1 2 annual payments, the first to be made one year after the loan is taken out. If / = .13, find the
Find the 17^^ term and the sum of the first 1 1 terms of each of the following:(a) The arithmetic sequence 2, 7, 12, 17, ....(b) The arithmetic sequence with a = 7\ and d = —3.(c) The arithmetic
Go to the Federal Reserve Board’s Web site at www.federalreserve.gov . Find the latest figures for financial assets outstanding at various types of financial institutions using the following steps.

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