This module is to provide an understanding of the fundamental concepts of financial mathematics, and how these concepts are applied in calculating present and accumulated values for various streams of cash flows. Students will also be given an introduction to financial instruments, such as derivatives, the concept of no-arbitrage.

  1. 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.

2. Derive formulae for all kinds of annuities

3. Given an annuity with level payments, immediate (or due) , payable m-thly, (or payable continuously), and any three of present value, future value, interest rate, payment, and term of annuity, calculate the remaining two items.

4. Given an annuity with non-level payments, immediate (or due) , payable m-thly, (or payable continuously), the pattern of payment amounts, and any three of present value, future value, interest rate, payment, and term of annuity, calculate the remaining two items.

5. Calculate the outstanding balance at any point in time.

6. Calculate a schedule of repayments under a loan and identify the interest and capital components in a given payment.

7. Given the quantities, except one, in a sinking fund arrangement calculate the missing quantity.

8. Calculate the present value of payments from a fixed interest security, bounds for the present value of a redeemable fixed interest security.

9. Given the price, calculate the running yield and redemption yield from a fixed interest security.

10. Calculate the present value or real yield from an index-linked bond.

11. Calculate the price of, or yield from, a fixed interest security where the income tax and capital gains tax are implemented.

12. Calculate yield rate, the dollar-weighted and time weighted rate of return, the duration and convexity of a set of cash flows.

13. Describe the concept of a stochastic interest rate model and the fundamental distinction between this and a deterministic model.

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

Pri ncipal, 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 i s 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

 6.       Term structure of interest rates & Stochastic  interest rates models

Par yield, yield to maturity, immunisation, explain the use of duration and convexity in the (Redington) immunisation of a portfolio of liabilities; the stochastic interest rate model, calculate the mean and variance of the accumulated amount  of a single premium/an annual premium, the distribution functions for the accumulated amount of a single premium and for the present value of a sum due at a given specified future time provided (1+i) is log-normally distributed, calculate the probability that a simple sequence of payments will accumulate to a given amount at  a specific future time