Dr Gelly Mitrodima COL.7.04

This course is compulsory on the BSc in Actuarial Science. This course is available on the BSc in Business Mathematics and Statistics and BSc in Statistics with Finance. This course is available as an outside option to students on other programmes where regulations permit and to General Course students.

Students must have completed Mathematical Methods (MA100) and Elementary Statistical Theory (ST102).

The application of compound interest techniques to financial transactions. Describing how to use a generalised cash-flow model to describe financial transactions such as a zero coupon bond, a fixed interest security, an index-linked security, cash on deposit, an equity, an interest only loan, a repayment loan, an annuity certain and others. The time value of money using the concepts of compound interest and discounting. Accumulation of payments and present value of future payments. Expressing interest rates or discount rates in terms of different time periods. Real and money interest rates .The calculation of the present value and the accumulated value of a stream of equal or unequal payments using specified rates of interest and the net present value at a real (possibly variable) rate of interest, assuming a constant rate of inflation. Compound interest rate functions; definitions and use. Equations of value with certain and uncertain payments and receipts; conditions for existence of solution. Describe how a loan may be repaid by regular instalments of interest and capital; flat rates and annual effective rates. Calculation of a schedule of repayments under a loan and identification of the interest and capital components of annuity payments where the annuity is used to repay a loan for the case where annuity payments are made once per effective time period or p times per effective time period and identify the capital outstanding at any time. Discounted cash flow techniques and their use in investment project appraisal; internal rate of return, discounted payback period, money-weighted rate of return, time-weighted rate of return, linked internal rate of return. The investment and risk characteristics of fixed-interest Government borrowings, fixed-interest borrowing by other bodies, shares and other equity-type finance derivatives. The analysis of compound interest rate problems; the present value of payments from a fixed interest security where the coupon rate is constant and the security is redeemed in one instalment, upper and lower bounds for the present value of a fixed interest security that is redeemable on a single date within a given range at the option of the borrower, the running yield and the redemption yield from a fixed interest security, the present value or yield from an ordinary share and a property, given simple (but not necessarily constant) assumptions about the growth of dividends and rents, the solution of the equation of value for the real rate of interest implied by the equation in the presence of specified inflationary growth, the present value or real yield from an index-linked bond, the price of (or yield from) a fixed interest security where the investor is subject to deduction of income tax on coupon payments and redemption payments are subject to the deduction of capital gains tax.

20 hours of lectures and 9 hours of seminars in the MT.

Students will be expected to give written answers to a number of problem sets.

J J McCutcheon & W J Scott, An Introduction to the Mathematics of Finance, Heinemann; Institute of Actuaries, Formulae and Tables for Actuarial Examinations. Core reading notes obtainable from the Institute of Actuaries.

Exam (100%, duration: 3 hours) in the LT week 0.