Answer:
To calculate the interest earned on an investment, we can use the formula:
A = P(1 + r)^t
Where A is the amount in the account after time t, P is the initial principal or deposit, r is the interest rate, and t is the time in years.
In this case, the initial deposit is $8,241.78, the interest rate is 5.5% (or 0.055 as a decimal), and the time is 31 days.
Since the interest is compounded daily, we need to calculate the number of compounding periods for 31 days, which is 31 days.
Therefore, the formula becomes:
A = 8241.78(1+0.055)^31
To calculate the interest earned, we will subtract the initial deposit from the final amount in the account
Interest = A - P
So the interest earned in 31 days will be:
$8241.78 * (1+ 0.055)^31 - $8241.78 = $35094.06