Final answer:
Using the formula for compound interest, $10,000 invested at a 4% annual interest rate for 2 years results in a final amount of $10,816 and an interest earned of $816. The options given in the question do not include this correct value, indicating a possible typo or misunderstanding.
Step-by-step explanation:
The question is asking to calculate the final amount and the interest earned when $10,000 is invested at a 4% annual interest rate for 2 years.
To solve this, we'll use the formula for compound interest, which is A = P(1 + r/n)(nt), where:
- P is the principal amount ($10,000)
- r is the annual interest rate (0.04)
- n is the number of times the interest is compounded per year (1, since it is compounded annually)
- t is the time the money is invested for in years (2)
The calculation is as follows:
A = 10,000(1 + 0.04/1)1(2) = 10,000(1.04)2 = 10,000 * 1.0816 = $10,816
Therefore, the final amount in the account after 2 years will be $10,816.
To find the interest earned, subtract the principal amount from the final amount:
Interest Earned = Final Amount - Principal = $10,816 - $10,000 = $816
The interest earned over the 2-year period will be $816.
However, when we compare it to the options provided in the question, there seems to be a mismatch between the calculated interest earned and the options given. None of the options correctly state $816 as the interest earned. The closest match is option a) with an interest earned of $416.32, which is incorrect. This discrepancy could be due to a possible typo in the options presented or a misunderstanding of the question's requirements.