Institute of Actuaries of India 2005 Subject CT1-Financial Mathematics Core Technical - Question Paper

1.Describe how cashflows are exchanged in an interest rate swap . [2]

2.An investor has earned a money rate of return from a portfolio of bonds in a particular
country of 1% per annum effective over a period of ten years. The country has
experienced deflation (negative inflation) of 2% per annum effective during the
period.
compute the real rate of return per annum over the ten years. [2]

3.Calculate the time in days for £1,500 to accumulate to £1,550 at:
(a) a simple rate of interest of 5% per annum
(b) a force of interest of 5% per annum[4]

4.The force of interest (t) at time t is a + bt2 where a and b are constants. An amount of
£200 invested at time t = 0 accumulates to £210 at time t = five and £230 at time t = 10.
Determine a and b. [5]

5.(i) compute the current value of £100 over ten years at the subsequent rates of
interest/discount:
(a) a rate of interest of 5% per annum convertible monthly
(b) a rate of discount of 5% per annum convertible monthly
(c) a force of interest of 5% per annum
[4]
(ii) A 91-day treasury bill is bought for $98.91 and is redeemed at $100.
compute the annual effective rate of interest found from the bill. [3][Total 7]

6.(i) State the features of a eurobond. [3]
(ii) An investor purchases a eurobond on the date of problem at a price of £97 per
£100 nominal. Coupons are paid annually in arrear. The bond will be
redeemed at par twenty years from the problem date. The rate of return from the
bond is 5% per annum effective.
(a) compute the annual rate of coupon paid by the bond.
(b) compute the duration of the bond.[6][Total 9]

. A bank makes a loan to be repaid in instalments annually in arrear. The first
instalment is 50, the 2nd 48 and so on with the payments reducing by two per annum
until the end of the 15th year after which there are no further payments. The rate of
interest charged by the lender is 6% per annum effective.
(i) compute the amount of the loan. [6]
(ii) compute the interest and capital components of the 2nd payment. [3]
(iii) compute the amount of capital repaid in the instalment at the end of the
fourteenth year. [3][Total 12]

8.An insurance company has just written contracts that require it to make payments to
policyholders of £1,000,000 in 5 years time. The total premiums paid by
policyholders amounted to £850,000. The insurance company is to invest half the
premium income in fixed interest securities that give a return of 3% per annum
effective. The other half of the premium income is to be invested in assets that have
an uncertain return. The return from these assets in year t, it, has a mean value of

Earning:   Approval pending.