Nominal Interest rate is the interest rate before taking inflation into consideration.
- It is also referred to as the ‘Stated’ interest rate as it is generally quoted in loan and deposit agreements.
- 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