invest $25,000 at 8% interest compounded continuously, what is the average amount in your account over one year?

thats cause your dumb

To calculate the average amount in your account over one year with continuous compounding, you need to use the formula A = P * e^(rt), where:

- A represents the final amount in the account
- P is the initial principal (amount you invest), which is $25,000 in this case
- e is Euler's number, approximately 2.71828
- r is the interest rate per time period, which is 8% or 0.08 as a decimal
- t is the time period, which is 1 year

Now let's calculate the average amount:
A = $25,000 * e^(0.08 * 1)

To get the exact average, we would need the exact value of e raised to the power of (0.08 * 1). However, for convenience, let's use an estimation of e^(0.08 * 1).

e^(0.08 * 1) is approximately 1.08328706767.

Now we can calculate A:
A = $25,000 * 1.08328706767 ≈ $27,082.17

Therefore, the average amount in your account over one year, when investing $25,000 at 8% interest compounded continuously, is approximately $27,082.17.

amount = 25000 e^(.08) = 27082.18

(I don't understand why they ask for the "average" amount)