Institute of Actuaries of India 2008 Subject CT1 – Financial Mathematics - Question Paper

Q. 3) compute an equivalent annual effective rate of interest on an investment that is
discounted for three months at a simple rate of discount of 7% per annum.
[3]
Q. 4) The market value of assets of a small pension fund at different times in the calendar year
2007 was as follows:
1January 2007 1April 2007 one July 2007 one October 2007 31 December 2007
1,000,000 1,160,000 1,200,000 1,280,000 1,260,000
There was a fresh investment of 200,000 on 31 March 2007 into the fund. For 2007,
calculate:
(i) The money-weighted rate of return for the fund
(ii) The time-weighted rate of return for the fund
(iii) The linked quarterly rate of return for the fund
(4)
(1)
(1)
[6]
IAI CT1 0508
Page three of 5
Q. 5) (i) List main features of Eurobonds
(ii) List main features of Index linked government bonds
(iii) define how cashflows are exchanged in an interest rate swap.
(iv) define briefly the risks faced by counterparty to an interest rate swap.
(3)
(3)
(2)
(2)
[10]
Q. 6) An investor purchased a bond with exactly 15 years to redemption. The bond is
redeemable at par and has a gross redemption yield of 5% per annum effective. It pays
coupons of 4% per annum, half yearly in arrear. The investor pays tax at 25% on the
coupons only.
(i) compute the price paid for the bond.
(ii) After exactly 8 years, immediately after the payment of the coupon then due,
this investor sells the bond to a different investor who pays income tax at a rate of
25% and capital gains tax at a rate of 40%. The bond is purchased by the second
investor to give a net return of 6% per annum effective.
compute the price paid by the 2nd investor.
(3)
(5)
[8]
Q. 7) (i) State the 3 conditions for Redington’s immunization against small modifications in
the rate of interest.
(ii) A pension fund has liabilities of Rs.5 million due in 17 years time and Rs. 8
million in 20 years’ time. The fund manager of the fund has only 2 zero
coupon assets to invest, 1 maturing in 15 years and a different in 23 years. The
current interest rate is eight % per annum effective.
compute the amount the manager will invest in every fund so that 1st two
conditions for immunization against small modifications in the rate of interest is met.

Earning:   Approval pending.