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Sta 2191: Financial Mathematics 1 Question Paper

Sta 2191: Financial Mathematics 1

Course:Actuarial Science In Insurance

Institution: Meru University Of Science And Technology question papers

Exam Year:2011

University Examinations 2011/2012
FIRST YEAR, SECOND SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE IN ACTUARIAL SCIENCE
STA 2191: FINANCIAL MATHEMATICS 1
DATE:DECEMBER 2011. TIME:2HOURS
INSTRUCTIONS :Answer question one and any other two questions
QUESTION ONE (30 MARKS)
•• (12)
a i. Calculate. S ____ at an effective rate of interest of 13% per annum. (3 marks)
5.5|
ii. Explain what your answer to (i) represents. (2 marks)
b.For a rate of interest of 7% per annum, convertible monthly, calculate :
i. The equivalent rate of interest per annum convertible half yearly (2 marks)
ii. The equivalent rate of discount per annum convertible monthly (2 marks)
c i. What is an annuity (1 mark)
___
ii.Define. a___ in words (1 mark)
n|
___
iii. Define the formula for. a___ (3 marks)
n|
d. A stock issued by an investment bank pays Kshs. 4.00 per annum in respect of every 100 units of stock held.
The interest payments are made at the end of each year. What would be a fair price for an investor who intends to hold the stock indefinitely to pay on January 1,2010 for 10,000 units of the stock, of the investor can earn 10% per annum on similar investments?
e. A loan of Kshs. 900.00 is repayment by equal monthly payments for 3 years, with interest payable at 18.50% per annum effective.
Calculate the amount of each monthly payment. (4 marks)
f. If p=70 ,R=120,I=5 and n=10. Find an approximated value for i by interpolation. (4 marks)
g. Complete the table below using the symbols :A (=yes) , B(=no) or C(=sometimes) .
Contract. Absolute amount of payments. Timing of payments known in advance
known in advance?
Zero -coupon bond
Fixed-interest security
Index -linked security
Equity

QUESTION TWO (20 MARKS)
(Ia) __
a.i. Define. n| (3 marks)
(Ia) __ •• n
ii.Show that. n| = a__ ___ nv
n|
________________
I
iii. A loan is repayable by an increasing annuity payable annually in arrears for 15 years. The repayment at the end of
the first years Kshs.3, 000.00 and subsequent payments increase by Kshs.200.00 each year. The repayments were calculated using a
rate of interest of 8% per annum effective. Calculate the original amount of the loan. (6 marks)
b. A project has an initial outlay of Kshs. 15,000.000 at the end of

Sta 2191: Financial Mathematics 1 Question Paper

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