first major examination -...

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King Fahd University of Petroleum & Minerals

First Major Examination

Faculty: Science Department: Mathematics

Semester: 171 Course Name: Financial Mathematics

Instructor: Abedalhay Elmughrabi Course No: AS 483

Exam Date: November 13th, 2017 Exam Time: 07:00 PM – 09:00 PM

Student Name: ID No.:

Question No. Question Full Marks Question Obtained Marks

1 5 points

2 5 points

3 5 points

4 5 points

5 10 points

6 10 points

7 10 points

8 10 points

9 10 points

10 10 points

11 10 points

12 10 points

Total 100

Obtained Total:

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Exam Instructions

1. Fill in all information required.

2. The exam is composed of 12 questions.

3. Answers without calculations/steps will receive zero marks.

4. Only the following is allowed to be on your desk: SOA approved calculator,

pen/pencil, eraser, and sharpener.

5. Calculators cannot be exchanged during the examination.

6. No use of smart devices with communications capabilities (mini laptops, pens,

watches, phones, etc.)

7. Cell phones must be turned off and placed under your bench facedown.

8. No questions are allowed during the exam.

9. All material related to the course should be put away

10. Be clean, neat and tidy, else your work may not be marked

11. Students must not communicate with one another in any manner whatsoever

during the examination.

GOOD LUCK

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Questions 1 (5 Points):

Tuition is due and you are out of money. Grandma feels sorry for you so she tells you that she

will pay your tuition as long as you promise to pay her back $100 at the end of each quarter

for 8 years. Grandma tells you that she is charging you a 6% effective annual yield. Grandma

also reveals that she is a Fellow of the society of Actuaries and that the present value of the

payments she is collecting from you is exactly equal to the tuition. How much tuition did

grandma pay for you?

a. 2500

b. 2878.37

c. 2365.54

d. 2234.67

e. 2539.13

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Question 2 (5 Points):

Your brother does not feel sorry for you. He is angry about all the teasing and grief you gave

him here while you were growing up. For all that pain and suffering, he is demanding that

you pay him $1,000 at the end of each year for 6 years. He invests that money at a nominal

annual rate of return of 12% compounded monthly. How much money he will he have

accumulated at the end of the 6th year?

a. 8256.25

b. 7653.35

c. 9100.54

d. 7234.51

e. 8500.1

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Your sister thinks your brother has a good idea. She also just read that actuaries make good

money. Wanting to get the fair share of your future salary, she is also demanding payments

from you. She would like payments at the end of each year for 7 years. The first payment

should be $1,000 and each subsequent payment will decrease by $100, for a total of 7

payments. What is the present value of this stream of payments at an effective annual yield of

4%?

a. 4768.98

b. 4672.45

c. 4295.49

d. 4189.78

e. 4287.11


6

Your parents are more reasonable that your siblings. They know how hard you are studying

and don’t want you to worry about having a job while in college. They know how hard you

are studying and don’t want you to worry about having a job while in college. They have told

you that they will give $1,000 spending money at the beginning of your first year in college.

They will increase that amount by 3.5% at the beginning of each future year in college to

keep up with inflation. If you invest that money at a nominal annual rate of interest of 8%

compounded quarterly, how much will you accumulate by the end of your 7th year when you

finally graduate?

a. 10,695.73

b. 11,236

c. 10,500.34

d. 9,897.22

e. 11,876.23


7

Your family has had enough of you for now, so just make your professor happy by finding

the present value of the following stream of payments if interest is credited at an annual

effective rate of 7%.


8

Jeff bought an increasing perpetuity due with annual payments starting at 5 and increasing by

5 each year until the payment reaches 100. The payments remain at 100 thereafter. The

annual effective interest rate is 4.5%. Determine the present value of this perpetuity?

a. 1530

b. 1555

c. 1580

d. 1610

e. 1565


9

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


10

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


11

A bank agrees to lend 10,000 now and X three years from now in exchange for a single repayment of

75,000 at the end of 10 years. The bank charges interest at an annual effective rate of 6% for the first

5 years and at a force of interest 𝛿𝑡 =1

𝑡+1 t ≥ 5. Calculate X.

a. 23,500

b. 24,000

c. 24,500

d. 25,000

e. 25,500


12

Carol and John shared equally in an inheritance. Using his inheritance, John bought a 10-year annuity-

due with an annual payment of $2,500 each. Carol put her inheritance in an investment fund earning

an annual effective interest of 11%. Two years later, Carol bought a 15 year annuity immediate with

annual payment of Z.

The present value of both annuities was determined using an annual effective interest rate of 7%.

Calculate Z?

a. 2350

b. 2465

c. 2495

d. 2540

e. 2876


13

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%


14

A loan of 20,000 is repaid by a payment of X at the end of each year for 10 years. The loan has an

annual effective interest rate of 11% for the first five years and 12% thereafter.

Calculate X. a. 2739.5

b. 3078.5

c. 3427.5

c. 3467.5

e. 3484.5

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