We will deal with 3 different rates: i Nom = nominal, or stated, or quoted, rate per year. i Per = periodic rate. EAR= EFF% = . effective annual rate.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
We will deal with 3 different rates:
iNom = nominal, or stated, or
quoted, rate per year.
iPer= periodic rate.
EAR= EFF% = .
8% quarterly: iPer = 8%/4 = 2%.
8% daily (365): iPer = 8%/365 = 0.021918%.
Our bank offers a Certificate of Deposit (CD) with a 10% nominal rate, compounded semi-annually. What is the true rate of interest that they pay annually (the effective annual rate)?
(1 + )
EFF% = - 1
How do we find EFF% for a nominal rate of 10%, compounded semiannually?
(1 + )
= - 1.0
= (1.05)2 - 1.0
= 0.1025 = 10.25%.
Any PV would grow to the same FV at 10.25% annually or 10% semiannually. In both instances, our money earns 10.25 percent each year.
12 percent compounded annually
EARs=(1 + 0.12/2)2 - 1= 12.36%.
EARM=(1 + 0.12/12)12 - 1= 12.68%.
EARD(365)=(1 + 0.12/365)365 - 1= 12.75%.
12 percent compounded semi-annually
12 percent compounded monthly
12 percent compounded daily
When using semi-annual periods we use the periodic rate:
Cpt = 134.01
When using annual periods we use the EAR:
Cpt = 134.01
The nominal rate is never used in calculations!
The use of the periodic rate and the effective annual rate is determined by the choice of N. If N is the number of years, the EAR is used. If N is the number of periods (shorterthan 1 year), the periodic rate is used. The nominal rate is not used in calculations. As shown later, the choice of N will be determined by the number of payments (PMT).
Written into contracts, quoted by banks and brokers. Not used in calculations or shown
on time lines.