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Additional tasks use given interest-rate tables with investment-year and portfolio-yield interpretations to rank 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QUESTIONS  \nCopyright 2005 by the Society of Actuaries and the Casualty Actuarial Society  \nSome of the questions in this study note are taken from past SOA/CAS examinations.  \nFM-09-05 PRINTED IN U.S.A.  \nThese questions are representative of the types of questions that might be asked of candidates sitting for the new examination on Financial Mathematics (2/FM) . These questions are intended to represent the depth of understanding required of candidates. The distribution of questions by topic is not intended to represent the distribution of questions on future exams.  \n1.  \nBruce deposits 100 into a bank account. His account is credited interest at a nominal rate of interest of 4% convertible semiannually.  \nAt the same time, Peter deposits 100 into a separate account. Peter’s account is credited interest at a force of interest of δ .  \nAfter 7.25 years, the value of each account is the same.  \nCalculate δ .  \n(A) 0.0388  \n(B) 0.0392  \n(C) 0.0396  \n(D) 0.0404  \n(E) 0.0414  \n2.  \nKathryn deposits 100 into an account at the beginning of each 4-year period for 40 years. The account credits interest at an annual effective interest rate of i.  \nThe accumulated amount in the account at the end of 40 years is X, which is 5 times the accumulated amount in the account at the end of 20 years.  \nCalculate X.  \n(A) 4695  \n(B) 5070  \n(C) 5445  \n(D) 5820  \n(E) 6195  \n3.  \nEric deposits 100 into a savings account at time 0, which pays interest at a nominal rate of i, compounded semiannually.  \nMike deposits 200 into a different savings account at time 0, which pays simple interest at an annual rate of i.  \nEric and Mike earn the same amount of interest during the last 6 months of the 8th year.  \nCalculate i.  \n(A) 9.06%  \n(B) 9.26%  \n(C) 9.46%  \n(D) 9.66%  \n(E) 9.86%  \n4.  \nJohn borrows 10,000 for 10 years at an annual effective interest rate of 10% . He can repay this loan using the amortization method with payments of 1,627 .45 at the end of each year. Instead, John repays the 10,000 using a sinking fund that pays an annual effective interest rate of 14% . The deposits to the sinking fund are equal to 1,627 .45 minus the interest on the loan and are made at the end of each year for 10 years.  \nDetermine the balance in the sinking fund immediately after repayment of the loan.  \n(A) 2,130  \n(B) 2,180  \n(C) 2,230  \n(D) 2,300  \n(E) 2,370  \n5.  \nAn association had a fund balance of 75 on January 1 and 60 on December 31. At the end of every month during the year, the association deposited 10 from membership fees. There were withdrawals of 5 on February 28, 25 on June 30, 80 on October 15, and 35 on October 31.  \nCalculate the dollar-weighted (money-weighted) rate of return for the year.  \n(A) 9.0%  \n(B) 9.5%  \n(C) 10.0%  \n(D) 10.5%  \n(E) 11.0%  \n6.  \nA perpetuity costs 77.1 and makes annual payments at the end of the year. The perpetuity pays 1 at the end of year 2, 2 at the end of year 3,   , n at the end of year (n+1) . After year (n+1), the payments remain constant at n. The annual effective interest rate is 10.5% .  \nCalculate n.  \n(A) 17  \n(B) 18  \n(C) 19  \n(D) 20  \n(E) 21  \n7.  \n1000 is deposited into Fund X, which earns an annual effective rate of 6% . At the end of each year, the interest earned plus an additional 100 is withdrawn from the fund. Atthe end of the tenth year, the fund is depleted.  \nThe annual withdrawals of interest and principal are deposited into Fund Y, which earnsan annual effective rate of 9% .  \nDetermine the accumulated value of Fund Y at the end of year 10.  \n(A) 1519  \n(B) 1819  \n(C) 2085  \n(D) 2273  \n(E) 2431  \n8.  \nYou are given the following table of interest rates:  \n\n| Calendar Year of Original Investment | Investment Year Rates (in %) |  |  |  |  | Portfolio\u003Cbr>Rates\u003Cbr>(in %) |\n| --- | --- | --- | --- | --- | --- | --- |\n| y | i 1y | i2y | i3y | i4y | i5y | iy+5 |\n| 1992 | 8.25 | 8.25 | 8.4 | 8.5 | 8.5 | 8.35 ","cbCailv4vC7aNyJC","https://ap.wps.com/l/cbCailv4vC7aNyJC","pdf",171918,85,"English","# Exam FM Financial Mathematics\n## Sample Questions (Representative Problem Types)","[{\"question\":\"What topics do the Financial Mathematics sample questions test?\",\"answer\":\"They test interest rate conversions and models (nominal convertible, force of interest, effective rates), plus standard actuarial cash-flow constructs like amortization, sinking funds, perpetuities, and accumulation with reinvestment.\"},{\"question\":\"How does the exam address comparisons between different interest structures?\",\"answer\":\"Several questions compare outcomes under different compounding assumptions, such as semiannual compounding versus force of interest or simple interest, and then require solving the unknown rate.\"},{\"question\":\"What does the question with the interest-rate table require?\",\"answer\":\"It asks to compute or compare accumulated values using different rate methodologies—investment year method, portfolio yield method, and reinvestment at the new money rate—then determine the ranking of the results.\"}]","EXAM FM - Financial Mathematics - Sample Questions | PDF",1790495844,214]