Final answer:
Using the compound interest formula, the correct answer for the compound interest earned on a $10,000 investment, at a 3% annual interest rate compounded monthly for 1 year, is $304.16.
Step-by-step explanation:
To calculate the compound interest earned on an investment amount (P) of $10,000, with an annual interest rate (r) of 3%, compounded monthly for 1 year, we will use the compound interest formula:
A = P(1 + r/k)kt
Where: A = the total amount in the account after interest P = the principal or initial amount invested ($10,000) r = the annual interest rate (0.03) k = the number of times interest is compounded per year (12) t = time in years (1)
Placing the values into the formula gives us:
A = $10,000(1 + 0.03/12)12(1)
A = $10,000(1 + 0.0025)12
A = $10,000(1.0025)12
A = $10,000(1.03042)
A = $10,304.16
The total future amount after 1 year is $10,304.16. The compound interest earned is the difference between the future value and the present value of the principal:
Compound interest = A - P
Compound interest = $10,304.16 - $10,000
Compound interest = $304.16
Therefore, the correct answer is a. $304.16.