CH 1
Normal vs Effective with e.g.
For example, if a bond pays 6% on an annual basis and compounds semiannually, then an investor who invests $1,000 in this bond will receive $30 of interest after the first 6 months ($1,000 x .03), and $30.90 of interest after the next 6 months ($1,030 x .03). The investor received a total of $60.90 for the year, which means that while the nominal rate was 6%, the effective rate was 6.09%. Mathematically speaking, the difference between the nominal and effective rates increases with the number of compounding periods within a specific time period.
Normal vs Effective e.g. 2
B#2: A nominal annual rate of interest of 6% compounded monthly i^(12) = 6% This is read as "i upper 12" meaning the interest rate is divided 12 => 6%/12 = 0.5%, which is the effective rate per month. The AV of a year under this scenario will be: (1 + i(m) / m ) ^m
Effective rate of interest
Effective annual interest rate is an investment's annual rate of interest when compounding occurs more often than once a year. r => (1+i/n)^n - 1 It uses power of compounding
Effective Rate of Discount (d.t)
It defines the rate of growth in an account based on the end of the year instead of the beginning. It can be expressed in terms of i.t. It helps us identify how much to pay now for an amount that is payable in the future i.e. PV [a(t) - a(t-1)] / a(t) The relationship b/w d.i. and pv variable (1-d)<=>v<=>1/(1+i) or i=>d/(1-d)
Nominal Rate of Interest
The nominal interest rate (also known as an Annualised Percentage Rate or APR) is the periodic interest rate multiplied by the number of periods per year. For example, a nominal annual interest rate of 12% based on monthly compounding means a 1% interest rate per month (compounded).
nominal to effective
if i(m) is the nominal annual rate compunded m times a year, then i(m)/ m is the effective rate for an m'th of a year & the AV of a year under this scenario will be: (1 + i(m) / m ) ^m to find the equivalent effective annual rate we :- (1 + i(m) / m ) ^m <=> 1+i and solve for i
