Suppose Ira invests $2,000 in an account that has an interest rate of 3% and is compounded continuously. What is the equation that models this situation, and how much money will the account have after 4 years? Round your answer to the nearest dollar.

A = 2000 e^ (0.03 t)

The account will have $2255 after 4 years

Step-by-step explanation:

* Lets talk about the compound continuous interest

- Compound continuous interest can be calculated using the formula:

A = P e^rt

# A = the future value of the investment, including interest

# P = the principal investment amount (the initial amount)

# r = the interest rate

# t = the time the money is invested for

- The formula gives you the future value of an investment, which is

compound continuous interest plus the principal.

- If you want to calculate the compound interest only, you need

to deduct the principal from the result, So, your formula is:

Compounded interest only = Pe^ (rt) - P

* Now lets solve the problem

- Ira invests $2,000 in an account

∵ P = $ 2000

- That account has an interest rate of 3%

∵ r = 3/100 = 0.03

- It is compounded continuously

∵ The equation of the compounded continuously is A = P e^rt

∴ A = 2000 e^ (0.03 t)

- We want to find the money in the account after 4 years

∵ t = 4

∴ A = 2000 e^ (0.03 * 4) = $2254.99 ≅ $2255

* The account will have $2255 after 4 years