Practice Test Questions. Exam FM: Financial Mathematics Society of Actuaries. Created By: Digital Actuarial Resources

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2 Practice Test Questions Exam FM: Financial Mathematics Society of Actuaries Created By: (Sample Only Purchase the Full Version) Introduction: This guide from (DAR) contains sample test problems for Exam FM offered through the Society of Actuaries. The book has over 00 practice questions to test your knowledge of the principles of interest rates. The problems encompass applications of interest rates in annuities, bonds, loans, and stocks. The set of questions is very comprehensive and attempts to cover all major topics featured on the actual test. Nearly all of these questions are math-based. Some of the examples require calculus, while others entail advanced algebra. You should expect to spend several days taking this test. There is no time limit. You can use your notes, textbooks, other actuaries, and whatever will help you answer the questions. These problems test your actuary skills and also attempt to teach you something. If you can correctly answer 7% of the questions (about 0 problems), you are prepared for the actual test. The first half of this guide contains the practice test questions. You should use your own scratch paper when taking the test so that you can retake it several times. The detailed solutions start on page 4. If you find any errors in the solutions or would like to debate an answer, please contact the Digital Actuaries. Copyright 007

3 (.) The balance in a savings account at time 4 is $,000. At time 3, the balance was $,600. What is the effective rate of interest during the fourth period? (6.) If the nominal rate of interest compounded monthly is 7.%, what is the annual effective rate of interest? (9.) An insurance company expects to collect $40 in premiums from a client in 7 months. The rate of interest compounded semi-annually is %. What is the present value of the premiums? (3.) Suppose the force of interest is defined by the following equations: δ r 0.04r, 0.00r for 0 r r, for 7 < r 0 What is the present value of $ to be paid in 0 years? (33.) What is the accumulated value in 0 years of an annuity paying $00 at the end of each year, with an annual effective interest rate of 4.3%? (47.) What is the price of a perpetuity immediate, ignoring mortality, that pays $60,000 every years with interest convertible annually at.4%?

4 3 (68.) An inflation-indexed retirement pension begins with a payment of $30,000 at the end of the first year. Each year, the payout rises by 4%. The employee is currently age 40, and payments begin at 6 and lasts exactly 0 years (guaranteed). If the company wishes to fully fund the annuity today, what will it cost? Assume i is 7% per annum. (7.) Suppose a project has the following inflows and outflows: Inflows: t Amount 4,000 4,00 6 8,000 0,000 Outflows: t Amount 0 0,000, ,000 What is the NPV of the project? Let i 6.%. (84.) Use the time-weighted method in the next example: The beginning account balance at time 0 is $0,000. Deposits to the account follow this schedule: t 3 C t 4,000 7,000 7,00

5 4 Interest credits follow this schedule: t 3 4 Interest 3,00 6,00 -,00 -,00 What is the annual effective yield rate? (37.) A bond has a redemption value of. The face value is.08, the coupon rate is 9.8% with annual coupons, and the term is 30 years. If the principal adjustment at time 7 is 0.0, find the YTM. (3.) Consider a bond with annual coupons. The book value after years is $780. The original owner of the bond resells it years and 39 days after its original sale. The flat price using the practical method is $843 at the time of the second sale. Find the flat price using the theoretical method at the new time. Use the actual/actual method for interest. (6.) On November, 00, an account opens with a balance of $0,000. On January, 0, the owner adds $6,000. On March, 0, the owner adds $X. On October, 0, the owner withdraws $8,00. The final balance on November, 0, is $4,30. Find X, if the annual effective interest rate over the year is 7.% computed with the dollar-weighted method.

6 Solutions (.) A(4) A(3),000, i A(3),600,600 (6.) i () 0.07 () i + i i + + i i.0744 i % (9.) i () 0.0 () i + i + + i.0 + i.006 i () i () i () i

7 6 () i p. v. 40 * * $437. *(7 /) (3.) r dr p. v. a (0) e r 0.00r dr * e r dr 7 [ 0.007r ] * r 0.00r dr r * r ( ) p. v. e $ ( * *0 ) 3 ( * * 7 ) ( ) ( ) (33.) 0 ( ) ac. v. s * 00 $, (47.) Price p. v. * 60, 000 i * s 0.04 s

8 7 p. v *.7 * 60,000 p.v. $99,48.3 (68.) k p. v. v *30,000* * 30,000 * $79,9. 0 (7.) NPV (p.v. of inflows) (p.v. of outflows) 6 p.v. of inflows 4,000v + 4,00v + 8,000v +,000v 3,7 + 3,84 +,483 +,860 $8,4 p.v. of outflows + 0,000 +,000v + 3,000v + 0,000 +,878 +,33 $4,0 4 0 NPV 8,4 4,0 NPV $3,944 (84.) Time: Contribution: 0 4,000 7,000 7,00 Fund Value: 0,000 3,00 3,700 9,00 34,600 Compound Rate: + j + j + j 3 + j 4

9 j B ' B ' + C 3,00 ' 0, j j B ' 3,700 B ' + C ' 3,00 + 4, B ' 9,00 ' 3, , B ' + C j B4 ' B ' + C 34,600 ' 9,00 + 7, ( + i ) ( + i ) 4 4 i *.08* 0.993* (37.) Fr g C PA ( g i) * v ( i) * ( + i) 4 f ( j) ( i)( + i) Let j 0.0, j j 0.0, f ( j ) , f ( j ) j j 0.0

10 9 (3.) B k with practical method 843 B * ( * i) ( * i) i f B. 904 with theoretical method 780 * ( + $84.73 f B ) (6.) i I A + C t * duration t A $0,000, B $4,30, C X,00 A + C + I B 0,000 + X,00 + I 4,30 I 6,80 X 6,80 X , ,000 * ( / 6) + X * (8 /) 8,00 * (/) 6,80 X , (8 /) * X 3, X 6, 80 X X,968. X $,833.0

You will also see that the same calculations can enable you to calculate mortgage payments.

You will also see that the same calculations can enable you to calculate mortgage payments. Financial maths 31 Financial maths 1. Introduction 1.1. Chapter overview What would you rather have, 1 today or 1 next week? Intuitively the answer is 1 today. Even without knowing it you are applying