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.

Accepted Solution

Answer:A = 2000 e^(0.03 t)The account will have $2255  after 4 yearsStep-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