1 Project 2- Stock Option Pricing Mathematical Tools -Today we will learn Compound Interest

2 Compounding Suppose that money left on deposit earns interest. Interest is normally paid at regular intervals, while the money is on deposit. This is called compounding.

3 Compound Interest Discrete CompoundingDiscrete Compounding -Interest compounded n times per year Continuous CompoundingContinuous Compounding -Interest compounded continuously

4 Compound Interest Compound Interest P- dollars invested r -an annual rate n- number of times the interest compounded per year t- number of years F- dollars after t years.

5 Discrete Compounding Example 1 What is the value of $74,000 after 3-1/2 years at 5.25%,compounded monthly?

6 Example1 (i) Using Discrete Compounding formula Given P=$74,000 r= n=12 t=3.5 Goal- To find F

7 Discrete Compounding Example 2 What is the value of $150,000 after 5 years at 6.2%, compounded quarterly?

8 Example 2 (i) Using Discrete Compounding formula Given P=$150,000 r=0.062 n=4 t=5 Goal- To find F

9 Compound Interest Continuous Compounding The value of P dollars after t years, when compounded continuously at an annual rate r, is F = P  e r  t

10 Continuous Compounding Example 1 Find the value, rounded to whole dollars, of $750,000 after 3 years and 4 months, if it is invested at a rate of 6.1% compounded continuously.

11 Example1 (i)Using Continuous Compounding formula Given P=$750,000 r=0.061 t=(40/12) Goal- To find F F = P  e r  t F = 750,000  e  (40/12) =$ 919,111