Financial Mathematics
Level H 3Fin 06 40444
Level M 4Fin 06 39842
Sample paper
May/June Examinations 2024–25
1. (a) Select one best answer from the options provided. You do not need to justify your answer.
(i) In a generalised cashflow model, the cashflows of an equity share are
(A) Fixed and known in advance
(B) Variable and uncertain
(C) Always negative
(D) Not relevant to the model
(ii) The primary reason for using models in actuarial science is to
(A) Eliminate all business risks
(B) Guarantee profit maximisation
(C) Predict future financial outcomes
(D) Simplify regulatory compliance [2]
(b) Calculate the present value of £100 due in five years at the following rates of inter-est/discount:
(i) a rate of discount of 4% per annum effective;
(ii) a rate of interest of 4% per annum convertible quaterly;
(iii) a rate of discount of 4% per annum convertible monthly.
Round your answers to 2 decimal places. [6]
(c) The force of interest δ(t) is a function of time, and at any time t (measured in years) it is given by the following formula:
Round your final answers to parts (i)–(iii) of this question to 2 decimal places.
(i) Calculate the accumulated value of a unit sum of money over 10 years.
(ii) Calculate the effective annual rate of interest over 10 years.
(iii) Calculate the present value at time t = 0 of a continuous payment stream that is paid at the rate of per unit time between t = 9 and t = 12. [11]
(d) In this question, you must calculate the answers using appropriate formulae involv-
ing annuities. For each part, write the final answer in pounds and pence.
Every 3 years £100 is paid into an account which earns interest at a constant rate. Find the accumulated amount of the account immediately before the sixth payment is made, given that the interest rate is
(i) 10% per annum effective;
(ii) 10% per annum convertible quarterly. [6]
2. A loan of £10, 000 is to be repaid over 10 years by a level annuity payable monthly in arrears. The amount of the monthly payment is calculated on the basis of an interest rate of 2% per month effective. When answering this question, use the formulae involving annuities where appropriate and round all non-integer numerical values to 2 decimal places.
(a) Find the monthly repayment. [3]
(b) Find the total capital repaid and the interest paid in the first year. [8]
(c) After which monthly repayment the outstanding loan will be less than 王5, 000? [4]
(d) For which monthly repayment the capital repayment part will first exceed the interest part? [4]
(e) Immediately after the 80th payment of interest and capital, the effective interest rate on the outstanding loan is reduced to 1% per month. Calculate the revised monthly repayment under the assumption that the loan is to be repaid by the originally scheduled date, i.e., 10 years from its commencement. [6]
3. (a) Consider the following two projects. The cash flows as well as the NPV and IRR for the two projects are given. For both projects, the required rate of return is 10%. What discount rate would result in the same NPV for both projects?
一 A rate between 0.00% and 10.00%.
一 A rate between 10.00% and 15.02%.
一 A rate between 15.02% and 16.37%.
Show all of your calculations. [10]
(b) For each of the following issues, indicate whether the price of the issue should be at the nominal value, above the nominal value, or below the nominal value. You should assume that each issue is redeemed at par.
[15]
4. (a) Describe the three forms of the Efficient Markets Hypothesis. [10]
(b) The 1-year forward rate of interest at time t = 1 year is 5% per annum effective. The gross redemption yield of a 2-year fixed-interest stock issued at time t = 0, which pays coupons of 3% per annum annually in arrears and is redeemed at 102, is 5.5% per annum effective. The issue price at time t = 0 of a 3-year fixed-interest stock bearing coupons of 10% per annum payable annually in arrears and redeemed at par is £108.9 per £100 nominal.
(i) Calculate the 1-year spot rate per annum effective at time t = 0.
(ii) Calculate the 1 -year forward rate per annum effective at time t = 2 years.
(iii) Calculate the 2 -year par yield at time t = 0. [15]