Question

I need help solving the equation

Answer 1

$7000 invested at 4% compounded continuously for 9 years yields approximately $10,026.55.

The formula for compound interest compounded continuously is given by:

`\[ A = P \cdot e^(rt) \]`

where:

- A is the amount after time t,

- P is the principal amount (initial investment),

- r is the annual interest rate (in decimal form),

- t is the time in years,

- e is the mathematical constant approximately equal to 2.71828.

In your case:

- P = 7000,

- r = 0.04 (4% expressed as a decimal),

- t = 9 years.

`\[ A = 7000 \cdot e^(0.04 \cdot 9) \]`

Let's calculate this:

`\[ A = 7000 \cdot e^(0.36) \]`

Using a calculator:

`A \approx 7000 \cdot 1.432364654 \\\[ A \approx 10026.55 \]`

So, after 9 years, the amount, rounded to the nearest cent, would be approximately $10,026.55.