Nominal Interest rate is the interest rate before taking inflation into consideration.

1. It is also referred to as the ‘Stated’ interest rate as it is generally quoted in  loan and deposit agreements.
2. This interest rate does not take into account the compounding periods.
3. General notation : $i^{(m)}$

Expected Real Interest rate = Nominal Interest rate – Estimated Inflation rate

Realized Real Interest rate = Nominal Interest rate – Actual Inflation rate

#### $i_{real} = \frac{ i_{nominal} -\pi}{1+\pi}$

Effective Interest rate is the interest rate that takes into account the compounding periods. General notation: $i$

$\left[1+\frac{i^{(m)}}{m}\right ]^{m} = i$

Interpreting nominal and effective interest rates:

1. When compounding period is NOT given, given interest rate is the Effective interest rate and compounding period assumed to be equal to the given time period

1. i=12% per year  => Effective interest rate is 12% per year compounded annually
2. i=2% per month =>Effective interest rate is 2% per month compounded monthly
3. i=3% per quarter => Effective interest rate is 3% per quarter compounded quarterly

2.When compounding period is given, given interest rate is the Nominal interest rate and compounding period is the given time period

1. i=12% per year  compounded semiannually => Nominal interest rate is 12% per year compounded semiannually
2. i=2% per month compounded monthly=>Nominal interest rate is 2% per month compounded monthly
3. i=3% per quarter compounded semiannually=> Nominal interest rate is 3% per quarter compounded semiannually

3. In general, Nominal rates are lesser than the Effective rates.

1. When lending agencies charge interest, they generally advertise the nominal rates which does not truly reflect the actual interest the borrower owes the agency after the full year of compounding.
2. When lending agencies pay interest (savings acct etc.), they generally advertise the effective rate which is higher than the  nominal rate.

Annual Percentage Rate [APR]

Annual rate of interest that does not take into account the compounding of interest for that year.

APR = Periodic rate x No. of periods in a year.

Interest charged = 1% per month => APR = 1% x 12 = 12%

Annual Percentage Yield [APY]

Annual rate of interest that takes into account the compounding of interest for that year.

APR = [(1+ Periodic rate)^# of periods ] – 1

Interest charged = 1% per month => APY = 1.01^12 – 1 = 12.68%

Nominal interest rate of 10% convertible semiannually  =>  $i^{(2)} = 0.1$   $m = 2$   and   $\frac{0.1}{2}$  is paid every 6 months