I am dealing with Interest Compounded Continuosly. I am looking for the balance after 10 years. The book shows that P(10) = 2oooe^0.08(10)

= 2000e^0.8
= $4451.08

My questions is how do you calculate 2000e^o.8 and end up with 4451.08?

e*0.8 is 2.25 according to my calculator.

Put this into the google search window..

2000*e^0.8

With no interest rate and no principal given, it's tough for us to know how to help you.

The interest rate is 8%.

On your calculator, put in 0.8, hit the e^x button, then multiply that by 2000. I get 4451.08.

I usually use 2000*{[(0.08/365)+1]^365}^10 which gives 4450.69
My calculator gives 4450.69 also when using the TVM mode.

john wants to save 1000$. If he has 750$ and invest it at 12% how long will it take him to obtain 1000? to the nearest day

To calculate the value of 2000e^0.8, you need to follow these steps:

Step 1: Understand the formula
The formula for continuously compounded interest is given by:
A = P * e^(r*t)

Where:
A is the final amount or balance after t years,
P is the principal amount (initial investment),
e is the base of the natural logarithm (approximately equal to 2.71828),
r is the interest rate (expressed as a decimal),
and t is the time period in years.

Step 2: Substitute the given values into the formula
In this case, the principal amount (P) is $2000, the interest rate (r) is 0.08, and the time period (t) is 10 years. Therefore, we substitute these values into the formula:
A = 2000 * e^(0.08 * 10)

Step 3: Simplify the expression
Next, we simplify the exponent 0.08 * 10, which gives us 0.8. Therefore, the expression becomes:
A = 2000 * e^0.8

Step 4: Calculate e^0.8
To calculate e^0.8, use a scientific calculator or software that supports exponential calculations. Evaluating this expression, we find that e^0.8 is approximately equal to 2.22554.

Step 5: Multiply the principal amount by e^0.8
Finally, multiply the principal amount ($2000) by e^0.8 to obtain the final balance:
A = 2000 * 2.22554
A ≈ $4451.08

Therefore, the balance after 10 years with continuous compounding, starting with an initial investment of $2000 at an interest rate of 8%, is approximately $4451.08.