An initial investment of $3,000 earns 7% interest compounded continuously. What will the investment be worth in 19 years? (Round your answer to the nearest cent.)

What is

3000 e^(.07*19) ?

(hint: it more than triples)

please help more i know it triples more but how do i figure it out

To find the future value of an investment with continuous compounded interest, we can use the formula:

A = P * e^(rt)

Where:
A = the future value of the investment
P = the initial investment amount
r = the interest rate (written as a decimal)
t = the time period in years
e = the base of the natural logarithm, approximately 2.71828

Given:
P = $3,000
r = 7% = 0.07 (as a decimal)
t = 19 years

Plugging in the values into the formula, we get:

A = 3000 * e^(0.07 * 19)

Using a calculator, we can calculate e^(0.07 * 19) as approximately 3.018834042.

A = 3000 * 3.018834042
A = $9,056.50 (rounded to the nearest cent)

Therefore, the investment will be worth approximately $9,056.50 in 19 years.

To find the value of the investment after 19 years, we can use the formula for continuous compound interest:

A = P * e^(rt)

Where:
A = the final amount (or value) of investment
P = the initial investment amount
e = Euler's number, approximately 2.71828... (a mathematical constant)
r = the interest rate (in decimal form)
t = the time period in years

In this case, the initial investment (P) is $3,000, the interest rate (r) is 7% or 0.07, and the time period (t) is 19 years.

Plugging these values into the formula, we get:

A = 3000 * e^(0.07 * 19)

To calculate this using a calculator, we need to find the value of "e" raised to the power of 0.07 multiplied by 19 first. Then, multiply the result by the initial investment of $3,000.

After performing the calculations, the investment will be worth approximately $9,032.38 in 19 years. (Rounded to the nearest cent)