(Papers) ACET Paper May 2015 "CT1 – Financial Mathematics"
(Papers) ACET Paper May 2015 "CT1 – Financial Mathematics"
Q. 1) The nominal rate of discount per annum convertible quarterly is 8%.
i) Calculate the equivalent force of interest.
ii) Calculate the equivalent effective rate of interest per annum.
iii) Calculate the equivalent nominal rate of discount per annum convertible
monthly.
Q. 2)
i) Briefly describe the Call and Put Options
ii) Compare the debenture stocks and unsecured loan stocks
Q. 3) A fixed interest stock bears a coupon of 7% per annum payable half yearly on 1st April and 1st October. It is redeemable at par on any 1st April between 1st April 2015 and 1st April 2021 inclusive at the option of the borrower.
On 1st July 2002 an investor purchased INR 10,000 nominal of the stock at a price to give a net yield of 6% per annum effective after allowing for tax at 25% on the coupon payments. On 1st April 2010 the investor sold the holding at a price which gave a net yield of 5% per annum effective to another purchaser who is also taxed at a rate of 25% on the coupon payments.
i) Calculate the price at which the stock was bought by the
investor.
ii) Calculate the price at which the stock was sold by him.
Q. 4) A continuous cash flow is to be paid at a rate of ρ(t) = 10 + 10t for 3 < t < 4 and ρ(t) = 50 – t 2 for 5 < t < 6. The force of interest applicable during the period is:
0.01 +
0.01t 0 ≤ t < 4
δ(t) = 0.15 – 0.003t2 4 ≤ t < 6
0.06 t ≥ 6
Find the total accumulated value of the above mentioned payment streams at time 10.
Q. 5) In a particular country, income tax and capital gains tax are both collected on 1st April each year in relation to gross payments made during the previous 12 months.
A fixed interest bond is issued on 1st January 2013 with a term of 25 years and is redeemable at 110%. The security pays a coupon of 8% per annum, payable half-yearly in arrears.
An investor, who is liable to tax on income at the rate of 25% per annum and at 30% per annum on capital gains, bought INR 10,000 nominal of the stock at an issue price of INR 9,900.
i) Assuming an inflation rate at 3% per annum over the term of the bond and assuming the investor holds the stock to redemption
a) Show that the money yield obtained by the investor is between
6% to 7% per annum
b) Also calculate the net real yield obtained by him.
ii) Explain how and why your answer to (i) above, would alter if tax were to be collected on 1st June instead of 1st April each year.