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principles of risk management

Questions and Answers of Principles Of Risk Management

▪ How does automation allow you to make mistakes easier and more comfortably?
▪ When the cart gets put before “two horses” in risk management, how do we put it back?
▪ What roles did Fyodor Dostoyevsky and Dr. Feynman play in risk management?
▪ What are the roles of the game changers and show‐stoppers in project risk management?
▪ What are the roles of broiler black swans and red herrings in risk management?
▪ What are the three (actually four) dimensions of risk management?
▪ What happens when projects do not have good risk management plans?
▪ What happens when projects do not have risk management plans?
▪ Is it really risk management? Or is it actually uncertainty management?
▪ When is a decision really a decision and when it is an opportunity?
▪ What are major uncertainty objects and their changers?
▪ What degrees of freedom do uncertainties have?
▪ Do we really know what we try to manage?
▪ What factors are behind deviations from the expected project outcome?
▪ What could be expected as a project outcome?
Let Oa)x denote the net single premium for a continuous life annuity (to a person age jc) which pays at the rate of / per year at the moment of attaining age x-\-t. (a) Explain why (T)x = tv' p,dt.
A 40-year-old purchases a life annuity with annual payments which will commence in exactly 10 years. The first payment is 1000 and payments will increase by 8% per year. If / = .08, show that the net
As with level life annuities, (Ia)x represents an increasing annuity where each yearly payment is divided into m equal payments paid at intervals of length ^. Derive the following approximate
Derive each of the following approximate formulae: (a) aax+(1-nEx) (b) ax (ax+x) (c) nax n\ax + nEx
Derive each of the following: m- -1 2m N(m) = m. (a) am) (b) nam) = = Nx+1 + N(m) x+n Dx Dx
Derive each of the following approximate formulae: (m) = (a) a (b) " (m) x:n\ == m-1 nlx - (m) nEx 2m x-(-1) (1-nEx) 2m
Determine which of the following expressions are equal to each other. (a) ax: xn+1 (b) x+ - Nx+ Dx x+n+1 (c) v" Px+n (d) nEx
Derive each of the following identities. (a) ax = vpx x+1 (b) ax=1+vpx x+1 (c) ax = x + 1 v" nPx - (d) nax = v" nPx ax+n (e) ax:n+m\ = = ax:m + vm mPx ax+m:n\ (f) Px-1 x=(1+i) ax-1
Find the net single premium for a life annuity of 5000 per year, with the first payment due in one year, sold to a 30-year-old in each of the following cases, (a) Px.96 for each x, and i = .09. (b)
Find the net single premium for a 28-year pure endowment of 20,000 sold to a male aged 36, in each of the following cases.Assume / = .12. (a) (b) l369618, 64 = 7100 164 Px .96 for all x (c) Px .98 if
Complete the missing entries in the following table.AppendixLO1 x lx dx Px 9x 1000 100 10 -234 5 750 300 6 0 .80 .60
(a) Find the duration and modified duration for the bond in Question 5.24(a).(b) Using the same notation as in the text, the method ofequated time gives a single-time value ofFind 1 for the bond in
In addition to the notation already introduced in this section, let k= ^^^andg- ^.(g) Apply Formula (5.5) to find the yield rate in Question 8.AppendixLO1 (a) Derive Makeham's Formula, which is g P =
Under an annuity, the first payment oin is made after one year, the second payment of « — 1 after two years, and so forth, until a payment of/? is made, after which payments cease. Show that the
Prove each of the following identities:AppendixLO1 (a) == (b) a = 1-e-no end (c) 3 ==
Let A be the balance in a fund on January 1, 1999, B the balance on June 30, 1999, and Cthe balance on December 31, 1999.(a) If there are no deposits or withdrawals, show that the dollarweighted and
Write a computer program which will take a given value of ^ and output the equivalent value of /. (Use the power series expansion.)AppendixLO1
(a) Write a computer program which will take a given value of /and output values oi f"^^ for a succession of values of w.(b) Extend the program in part (a) to also give you a value for (5, using b
Which is larger, i — 6 or 6 — d? Prove your answer.AppendixLO1
Show that.AppendixLO1 = di + d = i + d + i + ... 4 6
Show thatwhere D is the derivative with respect to /.AppendixLO1 D(8) = D A(1) - (81), A(t)
Prove that d < d^"^
Prove that /
Express J as a power series expansion in terms of/.AppendixLO1
Express v as a power series expansion in terms of 6.AppendixLO1
Using mathematical induction, prove that for all positive integers n, -^(v^'^S) = —(\ + i)(n — \)\, where -j- denotes derivative with respect to v.AppendixLO1
Obtain an expression for 6/ if^(0 — kd^^ b' c^'.AppendixLO1
Finda(/) if^, = .04(1 +0"^-AppendixLO1
Show that //w ^^ - .50.AppendixLO1
Assume that the force of interest is doubled.(a) Show that the effective annual interest rate is more than doubled.(b) Show that the effective annual discount rate is less than doubled.AppendixLO1
In Section 1.3, it was shown that for < / < 1, (1 + /y < 1 + it.Show that 1 + // — {\-\-iy is maximized at / = 4[/« / — In b].AppendixLO1
Find the equivalent value of (5 in each of the following cases.(a) /=.13(b) d=A3(c) /
(a) Prove that(b) Prove that.AppendixLO1 (w)P(w)! (w)P()
Prove that / > f^'>d^^\AppendixLO1
Show that.AppendixLO1 1-d. |- (5-1) 1^/^ ( 1 1 ) ( 05 + 1) = ($ + 1)^ (s)P ()
Express J^^^ as a function oi P\AppendixLO1
Find n such thatAppendixLO1 1+ (u) n 1+
100 grows to 107 in 6 months. Find each of the following:(a) The effective rate of interest per half-year.(b) P^ (c) / (d) J(3)AppendixLO1
The Bank of Newfoundland offers a 12% mortgage convertible semiannually. Find each of the following:(a) /• (b)^(^> (c)/
Phyllis takes out a loan of 3000 at a rate of 16% per year convertible 4 times a year. How much does she owe after 21 months?AppendixLO1
Acme Trust offers three different savings accounts to an investor.Account A: compound interest at 12% per year convertible quarterly.Account B: compound interest at 1 1 .97% per year convertible 5
The interest on L for one year is 216. The equivalent discount on L for one year is 200. What is Z?AppendixLO1
Four of the following five expressions have the same value (for/ > 0). Which one is the exception?AppendixLO1 (a) d (1-d) (b) (i-d) -V (c) (i-d)d (d) i - id (e) id
Prove each of the following identities mathematically. For parts(a), (b) and (c), give a verbal explanation of how you can see that they are correct.AppendixLO1 (a) d = iv (b) d=1-v (c) i-d = id (d)
Prove that dn is constant in the case of compound interest.AppendixLO1
(a) Sketch a graph oi a{t) with its extension to present value in the case of simple interest,(b) Explain, both mathematically and verbally, why 1 — it is not the correct present value t years in
Mary has 14,000 in an account on January 1, 1995.(a) Assuming compound interest at 12%) per year, find the present value on January 1, 1989.(b) Assuming compound discount at 12% per year, find the
Henry has an investment of 1000 on January 1, 1998 at a compound annual rate of discount d = .12.(a) Find the value of his investment on January 1, 1995.(b) Find the value of / corresponding to d.(c)
If 1 grows to ^ in X periods at compound rate / per period and 1 grows \o K'my periods at compound rate 2/ per period, which one of the following is always true? Prove your answer.(a) X 2y(d) y=
At a certain rate of compound interest, it is found that 1 grows to 2 in X years, 2 grows to 3 my years, and 1 grows to 5 in z years.Prove that 6 grows to 1 in z — x —y years.AppendixLO1
Annual compound interest rates are 13% in 1994, 11% in 1995 and 15% in 1996. Find the effective rate of compound interest per year which yields an equivalent return over the three-year
Find the accumulated value of 6000 invested for ten years, if the compound interest rate is 7% per year for the first four years and 1 1% per year for the last six.AppendixLO1
At a certain rate of simple interest, 1000 will accumulate to 1300 after a certain period of time. Find the accumulated value of 500 at a rate of simple interest # as great over twice as long a
(a) In how many years will 1000 accumulate to 1400 at 12%simple interest?(b) At what rate of simple interest will 1000 accumulate to 1500 in 6 years?(c) Repeat parts (a) and (b) assuming compound
Let A{t) be an amount function. For every positive integer n, define /„ = A(n) — A{n—\).(a) Explain verbally what /„ represents(b) Prove that A(n) - A(0) = h + h + ---¥ h-(c) Explain
Let a{t) be a function such that a(0) = 1 and /„ is constant for all n.(a) Prove that a{t) = (1 + iY for all integers / > 0.(b) Can you conclude that ait) = (1 + iy for all t > 0?AppendixLO1
Consider the function a(r) =(a) Show that a{0) = 1 and ^(1) = 1 + /.(b) Show that a(t) is increasing and continuous for / > 0.(c) Show that a(t) \ -\- it for t> 1.(d) Show that a(t) 1+ (+2i),
For the a{t) function given in Example 1.1, prove that /„+i < /„ for all positive integers n.AppendixLO1
Mary has 14,000 in an account on January 1, 1995.(a) Assuming compound interest at 11% per year, find the accumulated value on January 1, 2000.(b) Assuming ordinary simple interest at 11% per year,
Alphonse has 14,000 in an account on January 1, 1995.(a) Assuming simple interest at 8% per year, find the accumulated value on January 1, 2001.(b) Assuming compound interest at 8% per year, find the
After having made 6 annual payments of 500 each on a 3000 loan at 1 1% effective, with first payment one year after the loan was taken out, the borrower decides to repay the balance of the loan over
Find the price which should be paid for an annuity of 500 per year for the next 10 years, if the yield rate is to be 11% and if the principal can be replaced by a sinking fund earning 8% per year for
Ellen is repaying Friendly Trust a 10,000 loan with 8 equal annual payments of principal, the first due one year after the loan is taken out. In addition, she pays interest at 11% effective on the
Consider the transactions described in Question 32. Assume, in addition, that after 3 more payments, C sells his right to ftiture payments back to 5 at a price which yields B 20% effective on those
A borrows 1000 from B, and agrees to repay it in 8 equal installments at 18% effective, with the first payment due in one year. After 3 payments, B sells her right to future payments to C at a price
Ashley borrows 3000 for 10 years at 13% effective. She pays the interest yearly, and the principal by means of two sinking ftands.One-third of the principal is repaid by a sinking fund earning
Walter borrows 5000 for 20 years at 9% effective for the first 10 years and 11% effective for the last 10 years. He wishes to pay interest yearly and to repay the principal by annual payments into a
Kelly has borrowed 1000 on which she is paying interest at 11^%effective per year. She is accumulating a sinking fund at 9%effective to repay the loan. At the end of the eighth year, the borrower
A loan of 1000 is to be repaid by the sinking fund method over 10 years. The rates of interest on the loan and the sinking fund are /and /', respectively. The borrower's total payment each year is
A loan of 50,000 is taken out at 1 1% per year effective. Repayment is by the amortization method, with equal payments at the end of each year for the next 20 years. Immediately after the
A loan of 10,000 is taken out on March 1, 1995, at an effective rate of interest of 8% per year. Interest is paid annually, and a sinking fund is established to repay the principal on March 1, 2002.
Modify the program of Question 22 so that it can handle problems like Question 20. Test your program by redoing Question 20.AppendixLO1
Modify the program of Question 22 so that it can handle problems like Question 19. Test your program by redoing Question 19.AppendixLO1
Use the program of Question 22 to produce an amortization schedule for Question 7.AppendixLO1
Assuming a loan is to be repaid by equal payments, write a computer program which will output an amortization schedule for such a loan. Test your program by redoing Questions 17 and 18.AppendixLO1
Consider a loan which is being repaid by n equal annual payments of 1, the first due one year after the loan is taken out.(a) Assuming « > 5, construct the first 5 rows of the amortization
Construct an amortization schedule for the loan in Question 4.AppendixLO1
Construct an amortization schedule for the loan in Question 2.AppendixLO1
Construct an amortization schedule for the loan in Question 1.AppendixLO1
Henry borrows 5000 at 14% per year, and wishes to pay it back with 6 equal annual payments, the first due in one year. Construct an amortization schedule for this loan.AppendixLO1
Harriet is repaying a loan with payments of 3000 at the end of every two years. If the amount of interest in the 5^^ installment is 2,982.31, find the amount of principal in the 8'^
George was making annual payments ofXon a 16% 10-year loan.After making 4 payments, he renegotiates to pay off the debt in 3 more years with the lender being satisfied with 14% over the entire
The original amount of an inheritance was just sufficient at 8%effective to pay 5000 at the end of each year for 10 years. The payments of 5000 were made for the first 5 years even though the fund
In order to pay off a loan of ^, Herman makes payments ofXat the end of each year. Interest on the first B of the unpaid balance is at rate /, and interest on the excess is at rate/ Find the
A loan is being repaid with 20 annual installments of 1. Interest is at effective rate / for the first 1 years, and j for the last 1 years.Find an expression for each of the following:(a) The amount

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