Question

Arnold and Sandra invest the same amount of money in two different accounts that pay an interest rate compounded continuously. The amount that Arnold will earn after t years can be modeled by the expression Pe0.08t, and Sandra earns e0.004t times the amount Arnold earned in the same time. What is the interest rate compounded continuously that Sandra's account pays?

Answer 1

Using continuous compounding, it is found that Sandra's account pays an interest rate of 8.4%.

The amount of money, in continuous compounding, after t years, is given by:

$A(t) = A(0)e^{kt}$

In which:

• A(0) is the initial amount.

• k is the interest rate, as a decimal.

In this problem, Arnold's earnings are given by:

$A_A(t) = Pe^{0.08t}$

Sandra earns $e^{0.004t}$ times the amount Arnold earned in the same time, hence:

$A_S(t) = e^{0.004t} \times Pe^{0.08t} = Pe^{(0.08 + 0.004)t} = Pe^{0.084t}$

Comparing to the standard equation, Sandra's account pays an interest rate of 8.4%.

To learn more about continuous compounding, you can take a look at https://brainly.com/question/24722580