Question

how much would you have to deposit in an account with a 8% interest rate compunded continuously, to have $3000 in your account 10 years later

Answer 1

To have $3000 in your account 10 years later with an 8% interest rate compounded continuously, you would need to deposit approximately $1348.68.

Step-by-step explanation:

To find the amount you would have to deposit, we can use the formula for compound interest: A = P * e^(rt), where A is the amount accumulated, P is the principal (initial deposit), e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years.

In this case, we want to solve for P. We know that A = $3000, r = 8%, and t = 10 years. Plugging in these values, we have: $3000 = P * e^(0.08 * 10). Rearranging the equation to solve for P, we get:

P = $3000 / e^(0.8).

Using a calculator, we find that e^(0.8) ≈ 2.2255. So, P ≈ $3000 / 2.2255 ≈ $1348.68.