Final answer:
To calculate the interest Aaliyah earned after 2 years, the compound interest formula was used. The principal amount was found to be $10,200, and by subtracting this from the final account value of $11,236, the interest earned was determined to be $1,036, suggesting an error in the given options.
Therefore, the orrect option is a.
Step-by-step explanation:
The question involves compound interest which is a concept in mathematics where the interest earned is added to the principal, so that from that moment on, the interest that has been added also earns interest. To find the amount of interest Aaliyah earned after 2 years in an account with a 5% annual compound interest rate, given that the value of the account after 2 years is $11,236, we can use the compound interest 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 (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
We don't know the initial principal P, but we can solve for it because we have the other variables:
11,236 = P(1 + 0.05/1)^(1*2)
11,236 = P(1.05)²
11,236 = P(1.1025)
Now we divide both sides by 1.1025 to find P:
P = 11,236 / 1.1025
P = 10,200
The principal amount P is $10,200. The interest earned is the final amount minus the original principal:
Interest = A - P
Interest = 11,236 - 10,200
Interest = 1,036
So the amount of interest that Aaliyah earned after 2 years is $1,036, which is not one of the options provided. Therefore, there seems to be a mistake in the question or the options given are incorrect.
Therefore, the orrect option is a) $636