代做EXAM FM FINANCIAL MATHEMATICS代做留学生Matlab编程

日期：2024-09-27 06:14

EXAM FM ????FINANCIAL MATHEMATICS

EXAM FM SAMPLE QUESTIONS

This set of?sample questions includes those published on the interest theory topic?for use with???previous versions of?this examination. In addition, the following have been?added to reflect the revised syllabus beginning June 2017:

? ???Questions?155-158 on interest rate swaps?have?been?added.?Questions?155-157?are?from the?previous set of?financial economics questions. Question?158?is new.

? ???Questions 66,?178,?187-191 relate to the study note?on approximating the?effect?of?changes?in?interest rates.

? ???Questions?185-186 and?192-195 relate to the study note?on?determinants of?interest?rates.

? ???Questions?196-202 on interest rate?swaps were?added.

March 2018 – Question?157 has been deleted.

Some of?the questions in this study note are taken from past?SOA?examinations.

These?questions?are?representative?of?the?types?of?questions?that?might?be?asked?of?candidates

sitting for the Financial Mathematics (FM) Exam. ?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.

1.

Bruce deposits?100 into a bank account. ?His account?is?credited?interest?at?an?annual 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?an?annual?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

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.

(A)??????4695

(B) ??????5070

(C) ??????5445

(D)??????5820

(E)???????6195

3.

Eric deposits?100 into a savings account at?time?0,?which pays?interest?at?an?annual?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?8th?year.

Calculate i.

(A) 9.06%

(B) 9.26%

(C) 9.46%

(D) 9.66%

(E) 9.86%

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.

Calculate the balance in the sinking fund immediately after repayment of?the loan.

(A) 2,130

(B) 2,180

(C) 2,230

(D) 2,300

(E) 2,370

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%

6.

A perpetuity costs 77.1 and makes end-of-year payments. ?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%.

Calculate n.

(A)??????17

(B)???????18

(C)???????19

(D)??????20

(E)??????21

7.

1000 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. ?At?the?end?of?the??tenth year, the fund is?depleted.

The annual withdrawals of?interest and principal are deposited into?Fund Y,?which?earns?an?annual?effective?rate?of?9%.

Calculate the accumulated value of?Fund Y at the end of?year?10.

(A)??????1519

(B)???????1819

(C)??????2085

(D)??????2273

(E) ??????2431

8.?????????Deleted

9.

A 20-year loan of 1000 is repaid with payments at the end?of?each?year.

Each?of?the?first?ten?payments?equals?150% of?the?amount?of?interest?due.??Each?of?the?last?ten payments is X.

The lender charges interest at an?annual?effective rate?of 10%.

Calculate X.

(A)????????32

(B)????????57

(C) ????????70

(D)????????97

(E)???????117

10.

A?10,000 par value?10-year bond with?8% annual coupons is bought at a premium to yield?an?annual?effective?rate?of?6%.

Calculate?the?interest?portion?of?the?7th?coupon.

(A)??????632

(B) ??????642

(C) ??????651

(D)??????660

(E)???????667

11.

A perpetuity-immediate pays?100 per year. ?Immediately after the?fifth payment, the perpetuity is?exchanged?for?a?25-year?annuity-immediate?that?will?pay X at?the?end?of?the?first?year. ?Each subsequent annual payment will be 8% greater than the preceding payment.

The annual effective rate of?interest?is?8%.

Calculate X.

(A)??????54

(B)??????64

(C) ??????74

(D) ??????84

(E)???????94

12.

Jeff?deposits?10 into a fund today and 20 fifteen?years?later.??Interest?for the?first?10?years?is credited at a nominal discount rate of d compounded quarterly,?and thereafter at?a nominal interest rate of?6% compounded semiannually. ?The accumulated balance in the?fund?at the?end?of 30 years is?100.

Calculate d.

(A) 4.33%

(B) 4.43%

(C) 4.53%

(D) 4.63%

(E) 4.73%

13.

Ernie makes deposits of 100 at time 0, and X at time?3.??The?fund?grows?at?a?force?of?interest

δt = 100/t2, t >?0.

The?amount?of?interest?earned?from?time?3 to?time?6?is?also X.

Calculate X.

(A)??????385

(B)??????485

(C) ??????585

(D)??????685

(E)???????785

14.

Mike buys a perpetuity-immediate with varying annual payments. ?During the first 5 years, the?payment is constant and?equal to?10. ?Beginning in year?6,?the payments?start?to?increase.??For??year 6 and all future years, the payment in that?year?is K%?larger than the payment?in the?year???immediately preceding that year, where K < 9.2.

At an annual effective interest rate of?9.2%, the perpetuity has a present value?of 167.50.

Calculate K.

(A) 4.0

(B) 4.2

(C) 4.4

(D) 4.6

(E) 4.8

15.

A?10-year loan of?2000 is to be repaid with payments at the end of?each?year.??It?can be repaid?under the following two options:

(i) ???????Equal annual payments at?an?annual?effective?interest?rate?of?8.07%.

(ii) ??????Installments of?200 each year plus?interest?on the unpaid balance?at?an?annual?effective?interest?rate?of i.

The?sum?of?the?payments?under?option?(i) equals?the?sum?of?the?payments?under?option?(ii).

Calculate i.

(A) 8.75%

(B) 9.00%

(C) 9.25%

(D) 9.50%

(E) 9.75%

16.

A loan is amortized over five years with monthly payments at?an?annual?nominal?interest rate?of?9% compounded monthly. ?The first payment is?1000 and?is to be paid?one?month?from?the?date??of?the loan. ?Each succeeding monthly payment will be 2% lower than the prior payment.

Calculate the outstanding loan balance immediately after the 40th?payment is made.

(A)????6750

(B) ????6890

(C) ????6940

(D)????7030

(E)?????7340

17.

To accumulate 8000 at the end of?3n years,?deposits?of?98?are made?at the?end?of?each?of?the?first n years and?196 at the end?of?each?of?the next?2n years.

The annual effective rate of?interest is i.??You?are?given ?(1+ i)n = 2.0 .

Calculate i.

(A) 11.25%

(B) 11.75%

(C) 12.25%

(D) 12.75%

(E) 13.25%

18.

Olga?buys?a?5-year?increasing?annuity?for X.

Olga will receive 2 at the end of?the first month, 4?at?the?end?of?the?second?month,?and?for?each?month thereafter the payment increases by 2.

The annual nominal interest rate is 9% convertible?quarterly.

Calculate X.

(A)??????2680

(B)??????2730

(C)??????2780

(D)??????2830

(E) ??????2880

19.

You are given the following information about the?activity in two?different?investment?accounts:

Account K
Date	Fund value before activity	Activity
		Deposit	Withdrawal
January 1, 2014	100.0
July 1, 2014	125.0		X
October 1, 2014	110.0	2X
December 31, 2014	125.0

Account L
Date	Fund value before activity	Activity
		Deposit	Withdrawal
January 1, 2014	100.0
July 1, 2014	125.0		X
December 31, 2014	105.8

During 2014, the dollar-weighted (money-weighted) return for investment account K?equals?the?time-weighted return for investment account L, which equals i.

Calculate i.

(A)??????10%

(B)???????12%

(C)???????15%

(D)??????18%

(E) ??????20%

20.

David?can?receive?one?of?the?following?two?payment?streams:

(i)????????100 at time 0, 200 at?time n years,?and?300?at?time?2n years

(ii)???????600 at time?10?years

At an annual effective interest rate of i, the present values?of?the two?streams?are?equal.

Given vn = 0.76?, calculate i.

(A) 3.5%

(B) 4.0%

(C) 4.5%

(D) 5.0%

(E) 5.5%