First Major Examination -...
Transcript of First Major Examination -...
1
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:
2
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
3
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
4
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
5
Questions 3 (5 Points):
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
Questions 4 (5 Points):
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
Questions 5 (10 Points):
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%.
Questions 6 (10 Points):
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
Questions 7 (10 Points):
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
Questions 8 (10 Points):
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
Questions 9 (10 Points):
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
Questions 10 (10 Points):
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
Questions 11 (10 Points):
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%
Questions 12 (10 Points):