Final answer:
To calculate the interest rate of an investment that increased from $101 to $106.05 in one year, we find the total interest earned ($5.05) and divide it by the principal amount ($101), resulting in an interest rate of 5% per year.
Step-by-step explanation:
To determine the interest rate of an investment where the principal amount is $101 and it grew to $106.05 after one year, we need to use the formula for simple interest. The formula for simple interest is I = PRT, where I is the interest, P is the principal amount, R is the rate of interest, and T is the time period in years.
First, we calculate the interest earned, which is $106.05 - $101 = $5.05.
Next, we can rearrange the simple interest formula to find the rate (R): R = I / (PT). Since the time period (T) is 1 year, we can simplify our rate equation to R = I / P. Substituting the values, we get R = $5.05 / $101. Calculation gives us R = 0.05, which means the interest rate is 5% per year.