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