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FIM502S- FINANCIAL MATHEMATICST 1 -NOV 2019 |
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FACULTY OF HEALTH NAMIBIA UNIVERSITY
SCIENCES
OF SCIENCE AND TECHNOLOGY
AND APPLIED
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelor of science ; Bachelor of science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BSOC; 07BAMS
LEVEL: 5
COURSE: FINANCIAL MATHEMATICS 1
COURSE CODE: FIM502S
SESSION: NOVEMBER 2019
DURATION: 3 HOURS
SESSION: THEORY
MARKS: 100
EXAMINER
FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
Dr V. KATOMA
MODERATOR:
Dr S. EEGUNJOBI
INSTRUCTIONS
1. Answer ALL the questions in the booklet provided.
2. 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 [25 MARKS]
1.1 Derive compound interest formula from simple interest
[4]
1.2 Define nominal rates of interest
[2]
1.3 Derive the formula for continuous compounding from compounding interest
[6]
1.4 Define effective rates of interest
[3]
1.5 Blakely Investment Company owns an office building located in the commercial district
of Windhoek. As a result of continued success of an urban renewal program, local business
t
is enjoying a mini-boom. The market value of Blakely property is V(t) = 300,000Exp[* 2]
where V(t) is measured in dollars and t is the time in years from the present. If the
expected rate of appreciation is 9% compounded continuously for the next 10 years:
1.5.1 Find an expression for the present value P(t) of the market price of the property that
will be valid for the next 10 years.
[4]
1.5.2 Compute P(7), P(8) and P(9) and interpret the results.
[6]
QUESTION 2 [25 MARKS]
2.1 Show that —+jp.o——dl
[6]
so
a)
. _l-v"
2.2 Show that aa= d
[5]
2.3 Prove that a, = lim a,)=41/i
[5]
\\2
2.4 Demonstrate that So = a (1 + i)
[5]
2.5 Given that d = 6%, compute the value of / (12)
[4]
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QUESTION 3 [25 MARKS]
3.1 Define annuity
[3]
3.2 A loan of NS 10, 000.00 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 interest rate of 1% per
month effective. Find
3.2.1 The monthly repayment.
[6]
3.2.2 The total capital repaid and interest paid in the 1% and last years respectively.
[6]
3.3 A loan of NS 100 000.00 is being considered over a term of 10 years at an interest rate of
9% p.a. with monthly repayments. Repayments on loan are made at the end of the month,
so this is annuity immediate.
3.3.1 Construct an amortization table that shows the payments up to 6 months.
[6]
3.3.2 Calculate the total amount paid over the 10 years.
[4]
3.3.3 Calculate the amount of principle outstanding after 25° months.
[3]
QUESTION 4 [25 MARKS]
4.1 What is amortization?
[2]
4.2 An investor wishes to purchase a level annuity of NS 120.00 per annum payable
quarterly in arrear for five years. Find the purchase price, given that it is calculated on the
basis of an interest rate of 12% per annum
(a) Effective
[4]
(b) Convertible half-yearly
[4]
4.3 Chris is 35 years old and decides to start saving NS5000 each year, with the first deposit
one year from now. The account is awarding 8% p.a. Chris decides that he will make his last
deposit 30 years from now and hence retire at the age of 65. During retirement he plans to
withdraw funds from the account at the end of each year (first withdrawal at age 66).
4.3.1 What yearly amount will Chris be able to withdraw to last him to the age of 90?
[9]
4.3.2 If Chris’s bank above decides to change the interest rate to 9 : % in the last 10 years
of his turning 65, how much will he have in this account upon retirement?
[5]
--END OF EXAMINATION—
“aT R Soe