Question

Two people are placing a principal investment of 4,780 in separate accounts with 5.02% 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 12 years?

Answer 1

Account B uses simple interest which after 12 years results in a balance of $7659.35.

Step-by-step explanation:

The account that can be modeled exponentially is Account A, which uses continuously compounded interest. The formula for continuously compounded interest is given as A = Pert, where P is the principal, r is the annual interest rate, t is the time in years, and e is the base of the natural logarithm (approximately 2.71828).

Using this formula, the balance of Account A after 12 years is calculated as:

A = 4780e0.0502×12

A ≈ 4780 × 2.718280.6024 = 4780 × 1.82703

A ≈ $8741.46

As for Account B with simple interest, the balance of the account can be calculated using the formula A = P + (Prt), where A is the amount of money accumulated after n years, including interest. Therefore, the balance of Account B after 12 years is:

A = 4780 + (4780 × 0.0502 × 12)

A = 4780 + (4780 × 0.6024)

A = 4780 + 2879.35

A = $7659.35