Final answer:
To find the interest earned, use the formula for compound interest: A = P(1 + r/n)^(nt). Calculate the total amount after the specified time period and subtract the initial deposit to find the interest earned. The correct answer is c) $18.46.
Step-by-step explanation:
To find the interest earned, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the total amount after t years
- P is the principal amount (initial deposit)
- r is the annual interest rate (in decimal form)
- n is the number of times interest is compounded per year
- t is the number of years
In this case, the principal amount is 2310, the annual interest rate is 3 ½% or 0.035, the interest is compounded daily (365 times a year), and the time is from April 12 to July 5.
Using the formula:
A = 2310(1 + 0.035/365)^(365*(July 5 - April 12)/365)
We can calculate the total amount after the specified time period and then subtract the initial deposit to find the interest earned.
The correct answer is c) 18.46.