Actuarial Institute Papers

Can you provide me the Question Paper of Institute and Faculty of Actuaries as I am preparing for it?

[Arun Vats]

Here I am providing you some questions of Financial mathematics Exam paper April 2014 and for detail paper I am uploading a PDF attachment which you can download for free:

Subject CT1 - Financial mathematics Exam paper April 2014
1. Describe the main features of:
(a) debenture stocks.
(b) unsecured loan stocks. [5]

2. £900 accumulates to £925 in four months.
Calculate the following:
(i) the nominal rate of interest per annum convertible half-yearly [2]
(ii) the nominal rate of discount per annum convertible quarterly [2]
(iii) the simple rate of interest per annum [2]
[Total 6]

3. A company issues a loan stock bearing interest at a rate of 8% per annum payable
half-yearly in arrear. The stock is to be redeemed at 103% on any coupon payment
date in the range from 20 years after issue to 25 years after issue inclusive, to be
chosen by the company.
An investor, who is liable to income tax at 30% and tax on capital gains at 40%,
bought the stock at issue at a price which gave her a minimum net yield to redemption
of 6% per annum effective.
Calculate the price that the investor paid. [7]

4. An insurance company has liabilities of £10 million due in 10 years’ time and £20
million due in 15 years’ time. The company’s assets consist of two zero-coupon
bonds. One pays £7.404 million in 2 years’ time and the other pays £31.834 million
in 25 years’ time. The current interest rate is 7% per annum effective.
(i) Show that Redington’s first two conditions for immunisation against small
changes in the rate of interest are satisfied for this insurance company. [6]
(ii) Calculate the present value of profit that the insurance company will make if
the interest rate increases immediately to 7.5% per annum effective. [2]
(iii) Explain, without any further calculation, why the insurance company made a
profit as a result of the change in the interest rate. [2]
[Total 10]

5. Six months ago, an investor entered into a one-year forward contract to purchase a
non-dividend paying stock. The risk-free force of interest was 4% per annum. The
value of the stock is now 98% of its original value.
Calculate the minimum value for the risk-free force of interest at which the original
forward contract still has a positive value to the investor.

6. An insurance company borrows £50 million at an effective interest rate of 9% per
annum. The insurance company uses the money to invest in a capital project that pays
£6 million per annum payable half-yearly in arrear for 20 years. The income from the
project is used to repay the loan. Once the loan has been repaid, the insurance
company can earn interest at an effective interest rate of 7% per annum.
(i) Calculate the discounted payback period for this investment. [4]
(ii) Calculate the accumulated profit the insurance company will have made at the
end of the term of the capital project. [5]
[Total 9]

7. A loan of £20,000 is repayable by an annuity payable annually in arrear for 25 years.
The annual repayment is calculated at an effective interest rate of 8% per annum and
increases by £50 each year.
(i) Calculate the amount of the first payment. [3]
(ii) Calculate the capital outstanding after the first three payments have been
made. [2]
(iii) Explain your answer to part (ii). [2]
(iv) Calculate the total amount of interest paid over the term of the loan. [3]
[Total 10]

8. An investor is considering investing £18,000 for a period of 12 years. Let t i be the
effective rate of interest in the th t year, 12. t ≤ Assume, for 12, t ≤ that t i has mean
value of 0.08 and standard deviation 0.05 and that 1 t i + is independently and
lognormally distributed.
(i) Determine the distribution of 12 S where t S is the accumulation of £1 over t
years. [5]
At the end of the 12 years the investor intends to use the accumulated amount of the
investment to purchase a 12-year annuity certain paying:
£4,000 per annum monthly in advance during the first four years;
£5,000 per annum quarterly in advance during the second four years;
£6,000 per annum continuously during the final four years.
The effective rate of interest will be 7% per annum in years 13 to 18 and 9% per
annum in years 19 to 24 where the years are counted from the start of the initial
investment
(ii) Calculate the probability that the investor will meet the objective. [12]
[Total 17]

10 A loan of £20,000 is repayable by an annuity payable annually in arrear for 25 years.
The annual repayment is calculated at an effective interest rate of 8% per annum and
increases by £50 each year.
(i) Calculate the amount of the first payment. [3]
(ii) Calculate the capital outstanding after the first three payments have been
made. [2]
(iii) Explain your answer to part (ii). [2]
(iv) Calculate the total amount of interest paid over the term of the loan. [3]
[Total 10]