# FM-09-05ques - SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL...

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11/08/04 2 SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS Copyright 2005 by the Society of Actuaries and the Casualty Actuarial Society Some of the questions in this study note are taken from past SOA/CAS examinations.

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11/08/04 3 FM-09-05 PRINTED IN U.S.A.
11/08/04 4 These 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.

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11/08/04 5 1. Bruce deposits 100 into a bank account. His account is credited interest at a nominal rate of interest of 4% convertible semiannually. At the same time, Peter deposits 100 into a separate account. Peter’s account is credited interest at a force of interest of δ . After 7.25 years, the value of each account is the same. Calculate δ . (A) 0.0388 (B) 0.0392 (C) 0.0396 (D) 0.0404 (E) 0.0414
11/08/04 6 2. Kathryn 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 . The 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. Calculate X .

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11/08/04 7 3. Eric deposits 100 into a savings account at time 0, which pays interest at a nominal rate of i , compounded semiannually. Mike deposits 200 into a different savings account at time 0, which pays simple interest at an annual rate of i . Eric and Mike earn the same amount of interest during the last 6 months of the 8 th year. Calculate i .
11/08/04 8 4. John 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. Determine the balance in the sinking fund immediately after repayment of the loan.

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11/08/04 9 5. An 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. Calculate the dollar-weighted (money-weighted) rate of return for the year. (A) 9.0% (B) 9.5% (C) 10.0% (D) 10.5% (E) 11.0%
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