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FIM502S - FINANCIAL MATHEMATICS 1 - 1ST OPP - NOVEMBER 2023 |
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n Am I BIA u n IVE Rs ITY
OF SCIEnCEAnDTECHnOLOGY
FacultyofHealthN, atural
ResourceasndApplied
Sciences
Schoool f NaturalandApplied
Sciences
Departmentof Mathematics.
StatisticsandActuariaSl cience
13JacksonKaujeuaStreet
PrivateBag13388
Windhoek
NAMIBIA
T: +264612072913
E: msas@nust.na
W: www.nust.na
QUALIFICATION: BACHELOR of SCIENCE IN APPLIED MATHEMATICS AND STATISTICS
QUALIFICATION CODE: 07BSAM
LEVEL:5
COURSE:FINANCIAL MAHEMATICS 1
COURSECODE: FIM502S
DATE: NOVEMBER 2023
SESSION: 1
DURATION: 3 HOURS
MARKS: 100
EXAMINER:
MODERATOR:
FIRST OPPORTUNITY: QUESTION PAPER
Dr, Victor Katoma
Prot Adetayo Eegunjobi
INSTRUCTIONS
1. Answer all questions on the separate answer sheet.
2. Please write neatly and legibly.
3. Do not use the left side margin of the exam paper. This must be allowed for the
examiner.
4. No books, notes and other additional aids are allowed.
5. Mark all answers clearly with their respective question numbers.
PERMISSIBLE MATERIALS;
1. Non-Programmable Calculator
This paper consists of 3 pages including this front page
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Question 1 [25 Marks]
1.1 Define the following terms:
a) Effective rates of interest
[3]
b) Nominal rates of interest
[3]
c) Force of interest
[3]
1.2 Derive the formula for continuous compounding from compounding interest
[6]
1.3 Derive compound interest formula from simple interest rates
[5]
1.4 Define a sinking fund
[3]
1.5 Why do Banks charge interest
[2]
Question 2 [25 Marks]
2.1 Show that
[3]
2.2 Show that
-+1 z=-. 1
[7]
= -(12)
2.3 Given that d 6%, compute the value of Z
[8]
= 2.4 Given that o 0.1 find the values of i(4) and iC12 ).
[5]
2.5 Show that a"'] =1/i
[2]
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Question 3 [25 Marks]
3.1 Define Amortization or Loan Schedule
[3]
3.2 A loan of N$10, 000 is to be repaid over 10 years by a level annuity payable
monthly in arrears. The amount of the monthly payment is calculated on the basis of
an interest rate of 1% per month effective. Find the
3.2.1 Monthly repayment.
[4]
3.2.2 Total capital repaid, and interest paid in the first and last years.
[7]
3.2.3 Theinterestpaid in the finalyear
[3]
3.2.4 After which monthly repayment the outstanding loan is first
less than N$5, 000.
[8]
Question 4 [25 Marks]
4.1 As a savings program towards Alberto's college education, his parents decide to deposit N$100
At the end of every month into a bank account paying interest at the rate of 6% per year
compounded monthly. If the savingsprogram began when Alberto was 6 years old, how much
money would have accumulated by the time he turns 18?
(10]
4.3 Russa has purchased a farm worth N$50,000 through the bank. She has decided to pay
back the loan in yearly arrears instalments over 5 years. If money is worth 8% p.a.
schedule these payments on an amortization schedule.
(11]
4.3.1 Use <lnJ
Loan balance is N$ 22,331.51 [4]
to prove that after a third (3) payment the
ENDof EXAM
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