To calculate the effective annual rate (EAR) when interest is compounded semi-annually, you can use the following formula:
\[ \text{EAR} = \left(1 + \frac{i}{n}\right)^{n} - 1 \]
Where:
- \(i\) is the nominal interest rate (annual rate),
- \(n\) is the number of compounding periods per year.
For a nominal interest rate of 5.00% compounded semi-annually:
- \(i = 0.05\)
- \(n = 2\) (since it is compounded semi-annually)
Now, substituting these values into the formula:
\[ \text{EAR} = \left(1 + \frac{0.05}{2}\right)^{2} - 1 \] \[ = \left(1 + 0.025\right)^{2} - 1 \] \[ = (1.025)^{2} - 1 \] \[ = 1.050625 - 1 \] \[ = 0.050625 \text{ or } 5.0625% \]
So, the effective annual rate (EAR) is approximately 5.0625%.
If you want to input the values into a financial calculator, you typically would not use \(N\), \(PMT\), \(FV\), and \(PV\) for calculating the effective annual rate this way, because it's more of a formula-based calculation. Instead, use the formula directly to compute the answer.
However, if you're still looking to use a financial calculator for a related computation (e.g., compounding), you might input:
- \(N = 2\) (number of compounding periods per year)
- \(i/y = 5\) (the nominal interest rate)
- \(PV = -1\) (initial investment, like $1, to find out how much it grows)
- \(PMT = 0\) (since there are no additional payments)
- \(FV\) will then be calculated by the calculator based on these inputs.
However, for the EAR calculation, remember that it's mainly a derived output from the nominal rate and compounding frequency, so it's not typical to fill all of the inputs for that specific calculation.
1 answer