Acturial Science Question Paper

Acturial Science

Course:Bachelor Of Commerce

Institution: Kenyatta University question papers

Exam Year:2009

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2009/2010
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE

BMS 311: ACTUARIAL SCIENCE

DATE: Monday
28th December 2009

TIME: 2.00pm - 4.00pm

INSTRUCTIONS:
Answer question 1 and any other TWO questions

Question 1
a)
Kamau joined the staff pension scheme on 1st January 2008, the total monthly remittances (his and employer’s) to the scheme at the end of each of the last 12 months is Ksh 6,000. The fund manager has declared a rate of interest of 15%, compounded monthly for the year 2008. Determine the total amount to the credit of Kamau’s account as at 31st December 2008
[10marks]
b)
A bond of Ksh 5000,000 redeemable in 15 years at 105 pays 4% coupon. What is the purchase price to pay 6%. Show the accumulation of discount by schedule. [10marks]
c)
Using the English Life Table No. 12 for Males, find the probability of a person
aged 40;
i)
Surviving to age 50. [2marks]
ii)
Dying before age 50. [4marks]
iii)
Dying between the ages of 60 and 80. [4marks]

Question 2
a)
James wishes to borrow Ksh 10,000 for two years and to repay the loans plus interest at the end of the two years. Bank A charges interest on loans weekly at the nominal rate of 11% per annum. Bank B the charges interest on loan quarterly at the rate of 3% per quarter. Bank C charges interest for the first six months with a an annual effective rate of 3% and for the remaining period with an annual effective rate of 15%. In each case calculate the amount payable at the end of the two year period. Which bank should James choose for the loan? [10marks]
b)
Jane on retirement from a provident fund retains Kshs 300,000 and in addition purchases any annuity that pays 144 monthly payments of Ksh 8,000 each, the first due at the end of 5 years. If interest accrues at 9%. Compute the total amount received from the provident fund. [10marks]

Question 3
a)
ABC Company borrows Ksh 10,000,000 due in 15 years for the purpose of business expansion. If the bond agreement provides that Ksh 500,000 be raised from revenues and put in a fund each year, what rate of interest must be charged in order to pay off the principal of the debt at maturity? [10marks]
b)
Interest on certain deposits it compounded weekly. The annual effective rate is 15%. Find the nominal rate of interest per annum. Also obtain the accumulation of an investment of Ksh 5,000 over a period of 13 weeks. [10marks]

Question 4
a)
Compute the present value of an n year endowments of R to a person aged x. [10marks]
b)
Determine the effective rate, if the nominal rate is 7%, convertible continuously.[5marks]
c)
Roe win a prize which can be taken either as a lumpsum of Ksh 10,000 paid immediately or as monthly payment of Ksh 100 paid in advance for a ten year period. Assuming that interest stays at 4% per annum over this 10 year period. Which form of prize should she take. [5mark]

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