3. Compounding Interest The process where interest earns interest is called compounding interest. There are two types of compounding interest: Discrete compounding Continuous compounding 12/7/2018 Asitha Kodippili, Ph.D

3.1a) Discrete Compounding is the computation of interest at fixed intervals and addition of that interest to successive principals at the end of those fixed intervals. The fixed interval for computing interest is called the computation period. The frequency of compounding (compounding frequency) Is determined by dividing the length of the year by the fixed interval. 12/7/2018 Asitha Kodippili, Ph.D

3.1a) … Notations effective annual interest rate(%). number of compounding periods per year nominal rate of interest interest rate per period (periodic interest rate) number of years total number of periods Example : Annual interest rate of 8% compounded quarterly (or nominal rate of 8% convertible quarterly). 12/7/2018 Asitha Kodippili, Ph.D

3.1a) … From the definition of equivalency we have Because each side of the equation gives the accumulated value of 1 invested for a year. Therefore effective annual interest rate: 12/7/2018 Asitha Kodippili, Ph.D

3.1a) … Q1 An amount of money is invested for 5 years at a nominal rate of 6% convertible semiannually. Determine Compounding frequency the periodic interest rate the number of periods effective annual interest rate 12/7/2018 Asitha Kodippili, Ph.D

3.1b) Continuous compounding In continuous compounding interest is computed and added to the previous balance on continuing basis. However, actual addition of the interest occurs at discrete intervals. 12/7/2018 Asitha Kodippili, Ph.D