Questions: Given the annual interest rate and the compounding period, find i, the interest rate per compounding period. 8.2% compounded quarterly i= % (Type an integer or decimal rounded to the nearest thousandth as needed.)

Given the annual interest rate and the compounding period, find i, the interest rate per compounding period.
8.2% compounded quarterly
i= % (Type an integer or decimal rounded to the nearest thousandth as needed.)

Transcript text: Given the annual interest rate and the compounding period, find $i$, the interest rate per compounding period. $8.2 \%$ compounded quarterly $i=$ $\square$ \% (Type an integer or decimal rounded to the nearest thousandth as needed.)

Solution

Solution Steps

Step 1: Given Values

We are given the annual interest rate $ r = 8.2\% $ and the number of compounding periods per year $ n = 4 $ (quarterly).

Step 2: Calculate Interest Rate per Compounding Period

To find the interest rate per compounding period $ i $, we use the formula: \[ i = \frac{r}{n} \] Substituting the given values: \[ i = \frac{8.2}{4} = 2.05 \]

Step 3: Round the Result

We round $ i $ to the nearest thousandth: \[ i_{\text{rounded}} = 2.05 \]