Final answer:
To find out how much interest $5,579 earns in one day at a 7% interest rate compounded daily, apply the daily compound interest formula, adjust for one day's time period, and subtract the principal to find the interest earned.
Step-by-step explanation:
To calculate the amount of interest $5,579 would earn in one day at an interest rate of 7% when compounded daily, you need to use the formula for daily compound interest:
Amount = Principal \times (1 + \frac{rate}{number \space of \space times \space compounded})^{(number \space of \space times \space compounded \times time)}
In this case, the principal is $5,579, the time is 1/365 year (since it's just one day), the rate is 0.07 (as a decimal), and the number of times compounded is 365 (daily).
The setup for the equation would be:
Amount = $5,579 \times (1 + \frac{0.07}{365})^{(365 \times \frac{1}{365})}
However, if we are interested only in the interest earned in that one day, we would subtract the original principal from the total amount:
Interest earned = ($5,579 \times (1 + \frac{0.07}{365})^{(365 \times \frac{1}{365})}) - $5,579
After solving, this gives you the interest earned in a single day.