Nominal interest rate refers to the interest rate before taking inflation into account. Nominal interest rate can also refer to the advertised or stated interest rate on a loan, without taking into account any fees or compounding of interest. The nominal interest rate can be calculated using the formula:
\(r=im\),
where:
The effective interest rate (EIR), effective annual interest rate, annual equivalent rate (AER) (or simply effective rate) is the interest rate on a loan or financial product restated from the nominal interest rate and expressed as the equivalent interest rate if compound interest was payable annually in arrears. It can be calculated with the following formula:
\(i=(1+\frac{r}{m})^m−1\),
where:
Solution:
Since we're looking for the nominal rate of interest, we are determining \(r\). First, we can identify the information that is given in the problem:
\(m = 12\) (months per year), \(i=7.77\%=0.0777\)
We can use the effective interest rate formula, \(i=(1+\frac{r}{m})^m-1\), substitute the above values and solve for \(r\):
\(0.0777=(1+\frac{r}{12})^{12}-1\)
\(0.0777+1=(1+\frac{r}{12})^{12}\)
\(\sqrt[12]{1.0777}-1=\frac{r}{12}\)
\(r=12(\sqrt[12]{1.0777}-1) \approx 0.0751\)
So, the nominal rate of interest on a company that has a 7.77% EIR annually is \(7.51\%\).
Solution:
Since we're looking for the annual EIR, we are determining \(i\). First, we can identify the information that is given in the problem:
\(m = 12\) (months per year), \(r=21\%=0.21\)
We can use the effective interest rate formula, \(i=(1+\frac{r}{m})^m-1\), substitute the above values and solve for \(r\):
\(i=(1+\frac{0.21}{12})^{12}-1\)
\(i=(1+0.0175)^{12}-1\)
\(i \approx 0.2314\)
So, annual EIR the company charges is \(23.14\%\).