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FIM601S - FINANCIAL MATHEMATICS 2 - 2ND OPP - JULY 2022 |
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NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
FACULTY OF HEALTH, APPLIED SCIENCES & NATURAL RESOURCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelor of Science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BAMS
LEVEL: 6
COURSE CODE: FIM601S
COURSE NAME: Financial Mathematics 2
SESSION: JULY 2022
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
SUPPLEMENTARY/ SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER
Mrs. H. Y. Nkalle
Dr. V. Katoma
MODERATOR:
Prof. A.S. Eegunjobi
INSTRUCTIONS
1. Answer ALL the questions in the booklet provided.
Show clearly all the steps used in the calculations.
3. All written work must be done in blue or black ink and sketches must
be done in pencil.
PERMISSIBLE MATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPER CONSISTS OF 3 PAGES (Including this front page)
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Question 1
1.1 Define the Net Present Value?
[2]
1.2 Define the Internal Rate of Return?
[2]
1.3 Define Discounted Cash flow?
[2]
1.4 Zero-coupon bond?
[2]
Question 2
Name 4 Instruments in the money markets.
[4]
Question 3
Mention 3 ways in which Derivatives are used.
;
[6]
Question 4
(a) Write an expression to give the amount of interest earned from time t to time
t + sinterms ofA only.
(2]
(b) Use (a) to find the annual interest rate, i.e., the interest rate from the t years to
time t + 1 years.
[3]
Question 5
Calculate the present value of an annuity of amount NS 100.00 paid annually for 5 years at
the rate of interest of 9%.
[5]
Question 6
An investment of NS 200.00 returns N$ 120.00 at the end of 1%t year and NS 100.00 at the
end of 2" year, What is the internal rate of return (IRR)?
[5]
Question 7
An investor is able to borrow NS 1000.00 at 8% effective for one year and immediately
invest the NS 1000.00 at 12% effective for the same year. Find the investor’s Internal rate of
return on this Transaction.
[3]
Question 8
Frans is considering a project which requires an amount of N$3000.00 and another amount
of N$1000.00 after one year. In two years’, time, when the project ends, she expects an
inflow of N$4500.00. what is the internal rate of return (JRR) of this project? Is the above
Investment profitable? Assume that Frans can lend and borrow at the same fixed rate of
7.13% per annum.
[10]
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Question 9
Consider the following two cash-flow sequence:
Time (Year)
0
1
2
3
Project A
-80
96
1
5
Project B
-80
10
10
90
Show that NPV (A) > NPV (B) if the interest rate is r = 0.06 or 6%.
[10]
Question 10
Suppose a loan size of ly is repaid by nm equal installments at size x at times
“, a2 r S = n. Suppose the .interest rate charged bia s ia % per annum effectiv. e. Fi. nd an
expression for the capital repayment in the k“" installment.
[5]
Question 11
An investor is considering whether to invest in either or both of the following loans:
Loan A: For a purchase price of NS 20000, the investor will receive NS 1000 per annum
payable quarterly in arrear for 15 years.
Loan B: For a purchase price NS 11000, the investor will receive an income of NS605 per
annum, payable annually in arrear for 18 years, and a return of his outlay at the end of this
period.
The investor may borrow money at 4% per annum. Would you advise him to invest in either
loan, if so, which would be the more Profitable?
[10]
Question 12
A loan of $5000.00 is repaid by level annual payment over 3 years with the interest rate of
4%. Represent the loan schedule in a table form.
[10]
Question 13
Suppose an investor has a portfolio which includes security A and security B. The price at
time 0 are as follows: s, = 6 and sg = 11. He assesses the prices at time 1 will be Sf = 7
and S? = 14 if the market goes up and Sf = 5 and S? = 10 if the market goes down.
Check there is an arbitrage opportunity.
[5]
Question 14
Suppose certificates of deposit is issued with a face value of NS 500000.00 and a coupon of
6% for 90 days. After 30 days, its yield has fallen to 5.75%. What is the price?
[3]
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Question 15
Consider the cash flow sequence, a = (5,9,20,4,2),b = (6,7,3,1,36) at time t = 0,...,4.
Find the NPV of the cash flow assuming an interest rate of 7%.
[6]
End of paper
Total marks: 100
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