Question

Marta invests $8500 in a new savings account which earns 5.0% annual interest, compounded continuously. What will be the value of her investment after 5 years?

Answer 1

Given:

Investment = $8500

Rate of interest = 5.0%

Time = 5 years

Compounded continuously

To find:

The value of investment after 5 years.

Solution:

Rate = 5.0%

        $=\frac{5}{100}$

Rate = 0.05

Compound interest formula if interest compounded continuously:

$A = P e^{rt}$

where P is the investment and r is the rate and t is the time.

$A = 8500 \times e^{0.05 \times 5}$

$A = 8500 \times e^{0.25}$

The value of $e^{0.25}=1.284025$.

$A = 8500 \times 1.284025$

$A=10914.21$

The value of the investment after 5 years is $10914.21.