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

- It is also referred to as the
as it is generally quoted in loan and deposit agreements.**‘Stated’ interest rate** - This interest rate does not take into account the compounding periods.
- 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

- i=12% per year => Effective interest rate is 12% per year compounded annually
- i=2% per month =>Effective interest rate is 2% per month compounded monthly
- 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

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

- 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.
- 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