1. University of Economics, Faculty of Informatics Dolnozemská cesta 1, 852 35 Bratislava Slova k Republic Financial Mathematics in Derivative Securities and Risk Reduction Financial Mathematics Ass. Prof. Ľudovít Pinda, CSc. Department of Mathematics, Tel.:++421 2 67295 813, ++421 2 67295 711 Fax:++421 2 62412195 e-mail: pinda@dec.euba.sk

2. Sylabus of the lecture  Simple and compound interest.  Comparison simple interest with compound interest.  Nominal interest rates.  Accumulation factor, force of interest.  Stoodleys formula for the force of interest.  The basis compound interest functions.  Annuities-certain and annuities-due, present values and accumulations.  Continuously payable annuities.  Discounted cash flow, net present values.

3. Simple and compound interest K 0 – the amount in t = 0, K n – the amount in t =n, i – the interest rate p. a., n – the time of duration less then one year, d – the time of duration measured in days, K 0 n i – the interest of amount, K 0 n i KnKn K0K0 n t n – the time of duration is greater then one year,, Fig. 1

4. – the interest of amount, KnKn 1 t K0K0 Fig. 2

5. Comparison simple interest with compound interest Let K 0 =1 From the Binomic theorem From then,..

6. - the rate of interest for the period (the effective rate of interest for the period) KnKn n 0 = 1 n K0K0 Fig. 3

7. Nominal interest rates

10. Example 1.

11. Example 2. Solution.

13. Example 3. Solution.

14. Stoodley's formula for the force of interest Using: The model a smoothly decreasing or smoothly increasing force of interest. Situation:

15. Example 4 t = 0 the interest rate0.11, t = 4 the interest rate0.10, t = ∞ the interest rate0.08.,

16. The basis compound interest function Tab. 1

19. Continuously payable annuities

20. Discounted cash flow, net present values Example 5. Consider the cash flow an initial outlay of 20 000, after one year a futher outlay 10 000, an inflow of 3 000 per annum payable continuously for ten years beginning in three years' time and final inflow of 6 000 in the end of thirteen years' time. Express the net present value. Solution.

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