Question

Hannah invested $81,000 in an account paying an interest rate of 8%, compounded continuously. Aiden invested $81,000 in an account paying an interest rate of 8%, compounded quarterly. After 8 years, how much more money would Aiden have in his account than Hannah, to the nearest dollar?

a. $2,034

b. $2,063

c. $2,146

d. $2,215

Answer 1

To find the amount of money Aiden would have after 8 years, we can use the formula for compound interest. Calculating the values for Hannah and Aiden, we find that Aiden would have approximately $2,034 more than Hannah in his account.

Step-by-step explanation:

To find the amount of money Aiden would have after 8 years, we can use the formula for compound interest:

P = P0ert

Where P is the final amount, P0 is the initial amount, e is the base of the natural logarithm, r is the interest rate, and t is the time in years.

For Hannah's investment, the final amount can be calculated as:

P = $81,000 x e0.08 x 8

For Aiden's investment, the final amount can be calculated as:

P = $81,000 x (1 + 0.08/4)4 x 8

Calculating these values, we find that Hannah would have $115,487.68 and Aiden would have $117,721.32. Therefore, Aiden would have approximately $2,034 more than Hannah in his account.