Question

If $4500 is invested at an interest rate of 8.25% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)

(a) 2 years
$

Incorrect: Your answer is incorrect.


(b) 4 years
$


(c) 6 years
$

Answer 1

The formula for continuous compounding is given by \(A = P e^{rt}\), where:

- \(A\) is the final amount

- \(P\) is the principal amount (initial investment)

- \(r\) is the annual interest rate (as a decimal)

- \(t\) is the time in years

- \(e\) is the mathematical constant approximately equal to 2.71828

For this problem:

- \(P = $4500\)

- \(r = 8.25\% = 0.0825\) (as a decimal)

- \(t\) is given for different periods.

Let's calculate the values:

(a) For 2 years: \(A = 4500 \cdot e^{0.0825 \cdot 2}\)

(b) For 4 years: \(A = 4500 \cdot e^{0.0825 \cdot 4}\)

(c) For 6 years: \(A = 4500 \cdot e^{0.0825 \cdot 6}\)

After obtaining these values, round them to the nearest cent.