To determine the periodic interest rate for a nominal interest rate of 4.8% compounded monthly, follow these steps:
1. Convert the nominal interest rate to a decimal:
Take the given nominal annual interest rate and convert it from a percentage to a decimal. The nominal interest rate of 4.8% can be written as:
[tex]\[
\text{Nominal Rate} = \frac{4.8}{100} = 0.048
\][/tex]
2. Identify the number of compounding periods per year:
Since the interest is compounded monthly, there are 12 compounding periods in a year.
3. Calculate the periodic interest rate:
The periodic interest rate can be found by dividing the nominal annual interest rate (in decimal form) by the number of compounding periods per year. Using the formula:
[tex]\[
\text{Periodic Rate} = \frac{\text{Nominal Rate}}{\text{Number of Compounding Periods}}
\][/tex]
Substituting the values into the formula:
[tex]\[
\text{Periodic Rate} = \frac{0.048}{12}
\][/tex]
4. Simplify the calculation:
Perform the division to find the periodic rate:
[tex]\[
\text{Periodic Rate} = 0.004
\][/tex]
Therefore, the periodic interest rate for a nominal interest rate of 4.8% compounded monthly is:
[tex]\[
0.004
\][/tex]
This periodic rate represents the interest rate applied each month.
