Final answer:
The interest earned on Maxine's $1,000 deposit at 4.5% interest compounded semi-annually after 3 years is $141.06. However, this amount is not listed among the options provided in the question, which suggests a possible discrepancy in the question or the answer choices.
Step-by-step explanation:
To calculate the amount of interest earned from a deposit, we use the formula for compound interest. Since the interest for Maxine's deposit of $1,000 at a rate of 4.5% compounded semi-annually is to be calculated over 3 years, we will use the following formula:
A = P (1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
Plugging in the values, we get:
A = $1,000 (1 + 0.045/2)^(2*3)
This simplifies to:
A = $1,000 (1 + 0.0225)^6
A = $1,000 (1.0225)^6
A ≈ $1,000 * 1.14106
A ≈ $1,141.06
Maxine's account will have $1,141.06 after 3 years. To find the interest earned, we subtract the initial deposit from the total amount accumulated:
Interest Earned = A - P
Interest Earned = $1,141.06 - $1,000
Interest Earned = $141.06
Therefore, the correct answer for the amount of interest earned in 3 years is not listed among the provided options.