A continuously compounded account starts with $1500 in principal. The annual interest rate is 9.1%. What is the balance after 30 years?

Help please. Thanks

amount= 1500*e^.091*30= 1500 e^2.73

thanks

To calculate the balance of the continuously compounded account after 30 years, we can use the formula:

A = P * e^(r * t)

Where:
A = the final balance
P = the principal amount (initial amount)
e = the mathematical constant approximately equal to 2.71828 (base of the natural logarithm)
r = the annual interest rate (in decimal form)
t = the time period in years

In this case, P = $1500, r = 0.091 (9.1% expressed as a decimal), and t = 30 years. So, substituting these values into the formula, we get:

A = $1500 * e^(0.091 * 30)

Now we need to calculate e^(0.091 * 30) and then multiply it by $1500 to find the final balance.

To solve e^(0.091 * 30), we calculate e^(2.73). Here's how you can do it:

1. Start by calculating e^2.
- You can use a scientific calculator or a calculator with an exp or e^x function. Simply enter 2 and press the exp or e^x button. The result should be approximately 7.38906.

2. Multiply e^2 by itself, e.g., (e^2) * (e^2).
- Again, use your calculator to raise 7.38906 to the power of 2. The result should be approximately 54.59815.

3. Multiply the result from step 2 by e.
- Multiply 54.59815 by approximately 2.71828 (e). The result should be approximately 148.41316.

So, e^(2.73) is approximately 148.41316.

Now, we can calculate the final balance:

A ≈ $1500 * 148.41316
A ≈ $222,619.74

Therefore, the balance of the continuously compounded account after 30 years will be approximately $222,619.74.

To find the balance after 30 years in a continuously compounded account, you can use the formula:

balance = principal * e^(rate * time)

In this case, the principal is $1500, the interest rate is 9.1%, and the time is 30 years.

Substituting the values into the formula, we get:

balance = 1500 * e^(0.091 * 30)

Using a scientific calculator or an online calculator, we can calculate e^(0.091 * 30) to be approximately 63.6895.

Therefore, the balance after 30 years would be:

balance = 1500 * 63.6895
balance ≈ $95,534.25