Final answer:
To calculate the compound interest earned on a deposit, the formula P(1 + r/n)^(nt) is used. Here, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t represents the time in years. The exact amount can be found by substituting the necessary values into the formula.
Step-by-step explanation:
Finding Compound Interest Earned
The student is asking how to calculate the interest earned on a $2750 deposit with a 3 ½% interest rate, compounded daily, from June 12 to August 30. To determine this, we will use the formula for compound interest, which is P(1 + r/n)^(nt), where P is the principal amount ($2750), r is the annual interest rate (0.035), n is the number of times that interest is compounded per unit t, and t is the time the money is invested or borrowed for, in years.
For daily compounding, n is 365, since there are 365 days in a year. The time period, t, is the number of days from June 12 to August 30, which we need to count.
Step 1: Count the number of days from June 12 to August 30.
Step 2: Use the time in years (time in days divided by 365) in the compound interest formula to find the new balance after interest.
Step 3: Subtract the original amount ($2750) from the new balance to find the compound interest earned.
Without the actual counts of days, we are unable to provide the exact amount earned, but the student can follow these steps with a calendar to determine the correct answer from the options provided.