Engineering Economics Lecture # 4 Nominal and effective interest rates EAIR Payment period Compounding periods

Time For Calculation of Interest One Year –365 days –52 weeks –12 months –3 quarters (1 quarter = 3 months) Interest can be computed more frequently than one time a year Interest may be computed annually, semi annually, quarterly, monthly, weekly, daily, or any other time period selected

Nominal Rate Nominal means "in name only". This is sometimes called the quoted rate. Periodic Rate The amount of interest you are charged each period, like every month. Effective Annual Rate The rate that you actually get charged on an annual basis. Remember you are paying interest on interest. Let's say I give you a credit card and the interest rate on the card is 3% per month. What is the annual rate that you are actually charged? 36%? Well, no. It's actually 42.57%.

Calculation of Effective Interest Rates The Nominal Rate is 36%. The Periodic Rate is 3% (you are charged 3% interest on your balance every month) The Effective Annual Rate is 42.57% Nominal Rate = Periodic Rate X Number of Compounding Periods Nominal Rate = 3 x 12 = 36 % Effective Annual Rate = (1+ i / m) m -1 –m = the number of compounding periods –i = the nominal interest rate Effective Annual Rate = ( / 12 ) Effective Annual Rate = (1.03) Effective Annual Rate = (1.4257) -1 Effective Annual Rate =.4257 Effective Annual Rate = %

An interest rate is called nominal if the frequency of compounding (e.g. a month) is not identical to the basic time unit (normally a year) A Nominal Interest Rate is an interest Rate that does not include any consideration of compounding

Mathematically we have r = (interest rate per period) (No. of Periods)

An Effective interest rate is a true interest rate It is a rate that applies for a stated period of time It is conventional to use the year as the time standard So, the EIR is often referred to as the Effective Annual Interest Rate (EAIR) The EAIR is the true, annual rate given a frequency of compounding within the year

Effective Interest Rates Rate of interest for a given period i % per period (e.g. 7% per year, 1% per month) True cost of a loan True return on an investment

Which One to Use: “r” or “i e ”? Period

Example: EAIR given a nominal rate

EAIR’s for 18% nominal rate

Payment Period (PP) Recall: CP is the “compounding period” PP is now introduced: PP is the “payment period” Why “CP” and “PP”? Often the frequency of depositing funds or making payments does not coincide with the frequency of compounding

Remember For larger benefits CP = PP