Final answer:
To calculate the difference in the amounts with annual and quarterly compounding, we can use the formula A = P(1 + r/n)^(nt). After calculating the amounts with annual and quarterly compounding, we find a difference of $7.72. The correct answer is A. $7.56. Correct option is A.
Step-by-step explanation:
To calculate the amount of money you will have in 10 years with compound interest, we can use the formula:
A = P(1 + r/n)^(nt)
Where A is the final amount, P is the principal amount ($100 in this case), r is the annual interest rate (10% in this case), n is the number of times interest is compounded per year (4 for quarterly compounding), and t is the number of years (10 in this case).
First, let's calculate the amount with annual compounding:
Aannual = 100(1 + 0.10/1)^(1*10) = $259.37
Now, let's calculate the amount with quarterly compounding:
Aquarterly = 100(1 + 0.10/4)^(4*10) = $267.09
The difference in the amounts is $267.09 - $259.37 = $7.72. Therefore, the correct answer is A. $7.56.