Final answer:
To find the interest rate for the growth of an investment from $73,269.73 to $73,566.61 in a month, you calculate the interest earned and divide by the initial balance and the number of periods. The monthly interest rate is approximately 0.4862%, which translates to an annual rate of about 5.8% when multiplied by 12.
Step-by-step explanation:
The question asks us to determine the interest rate at which an account invested in a money market fund grew from $73,269.73 to $73,566.61 in a month. To calculate the monthly interest rate, we need to use the formula for simple interest:
I = P × r × t
Where I is the interest earned, P is the principal amount (initial investment), r is the rate of interest per period, and t is the time period the money is invested for.
Firstly, we calculate the interest I earned in that month:
I = Final Balance - Initial Balance
I = $73,566.61 - $73,269.73
I = $296.88
Next, we write the formula with the values we know (assuming t is 1 month or 1/12 of a year):
$296.88 = $73,269.73 × r × (1/12)
We solve for the monthly interest rate r:
r = ($296.88 / $73,269.73) × 12
After calculating, we find:
r = 0.004862 or 0.4862%
To express it as an annual rate, we would multiply by 12 (since there are 12 months in a year):
Annual Interest Rate = 0.4862% × 12
Annual Interest Rate = 5.8344%
Thus, the annual interest rate is approximately 5.8% to the nearest tenth.