Module Catalogues, Xi'an Jiaotong-Liverpool University

Module Code: MTH120
Module Title: Theory of Interest
Module Level: Level 1
Module Credits: 5.00
Semester: SEM2
Originating Department: Mathematical Sciences
Pre-requisites: N/A

 Aims Students gain a thorough understanding of the quantitative applications of interest and related functions. Students are required to understand how to price various financial instruments for different interest.
 Learning outcomes A Understand and calculate all kind of rates of interest, find the future value and present value of a cash flow, and write the equation of value given a set of cash flows and an interest rate.B Derive formulae for all kinds of annuities; understand the notation of annuities and formulas for the present value of financial derivativesC Calculate the outstanding balance at any point in timeD Calculate a schedule of repayments under a loan and identify the interest and capital components in a given payment; Given the quantities, except one, in a sinking fund arrangement calculate the missing quantity; Calculate the present value of payments from a fixed interest security, bounds for the present value of a redeemable fixed interest security; E Given the price, calculate the running yield and redemption yield from a fixed interest security. F Calculate the present value or real yield from an index-linked bondG Calculate the price of, or yield from, a fixed interest security where the income tax and capital gains tax are implementedH Calculate yield rate, the dollar-weighted and time weighted rate of return, the duration and convexity of a set of cash flows. I Describe the concept of a stochastic interest rate model and the fundamental distinction between this and a deterministic model.
 Method of teaching and learning This module is delivered through formal lectures and tutorial classes
 Syllabus 1. Time value of money Simple interest, compound interest, force of interest, the effective and nominal rates of interest, accumulated and discount factors, m-thly convertible rate of interest, future value, present value/net present value, inflation and real rate of interest, the general cash flow 2. Annuities Present value and accumulated value of annuity-immediate, annuity-due, annuity- immediate/due payable m-thly, continuous annuity and respective deferred annuities; increasing/decreasing annuities-immediate/due, increasing continuous annuities-immediate/due, and respective deferred annuities; and perpetuity 3. Loans and the equation of value Principal, interest, term of loan, outstanding balance, final payment (drop payment, balloon payment), amortization, sinking fund, the prospective and the retrospective methods; the equation of value for certain and uncertain payments and receipts, respectively 4. Cash flow models & Investment projects Yield rate, current value, duration, cash flow techniques for investment projects, the time-weighted/money-weighted rate of return, spot rates, forward rates, yield curve, convexity, portfolio and investment year allocation methods 5. Bonds, Fixed interest security and index-linked security Premium, redemption value, par value, term of bond; present value of payments from a fixed interest securities when the redemption is in one instalment and the coupon rate is constant; upper and lower bounds for the present value of a fixed interest security that is redeemable on a single a date within a given range; calculate price/running yield/redemption yield of a fixed interest security, index-linked bonds under a rate of inflation; arbitrage; price a forward contract in an arbitrage free environment; the value of a forward rate at any time during the term of the contract; hedging implied by a forward contract
Delivery Hours
 Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total Hours/Semester 39 13 98 150

## Assessment

 Sequence Method % of Final Mark 1 Assignments 15.00 2 Midterm Exam 15.00 3 Final Exam 70.00
 Module Catalogue generated from SITS CUT-OFF: 6/5/2020 9:04:50 PM