Question

Two people are placing a principal amount of $800 in a savings account with 6.5% annual interest. Account A uses continuously compounded interest, while Account B uses simple interest. Which account can be modeled exponentially, and what is the balance after 3 years?

1) Account A can be modeled exponentially, and the balance after 3 years is $...
2) Account B can be modeled exponentially, and the balance after 3 years is $...
3) Both Account A and Account B can be modeled exponentially, and the balance after 3 years is $...
4) Neither Account A nor Account B can be modeled exponentially.

Answer 1

The correct answer is that Account A, which uses continuously compounded interest, can be modeled exponentially. The balance in Account A after 3 years is approximately $982.34. Account B uses simple interest and can be modeled linearly, with a balance of $962.00 after 3 years.

Step-by-step explanation:

Among the two accounts described, Account A can be modeled exponentially. This is because Account A uses continuously compounded interest, which follows an exponential growth pattern. To calculate the balance after 3 years for Account A, you would use the formula A = Pert, where P is the principal amount, r is the annual interest rate (as a decimal), and t is the time in years. Using this formula:

A = $800e(0.065)(3)

After calculating, the balance in Account A after 3 years will be approximately $982.34.

In contrast, Account B uses simple interest which can be modeled linearly, not exponentially. The balance after 3 years for Account B can be calculated using the formula A = P(1 + rt). Applying this to Account B:

A = $800(1 + (0.065)(3))

This gives a balance of $962.00 after 3 years. Therefore, the correct answer is:

1. Account A can be modeled exponentially, and the balance after 3 years is $982.34.
2. Account B can be modeled linearly, and the balance after 3 years is $962.00.