Question

Initial of 2300 in an account at interest rate of 3% per year, compounded continuously. Assuming that no withdrawals are madefind the amount in the account after six years.Do not round any intermediate computations, and round your answer to the nearest cent

Answer 1

Answer:

$2753.60.

Explanation:

For an initial amount, A(0) compounded continuously, The amount in the account, A(t) after t years at a rate of r% is:

$A(t)=A_0e^{rt}$

In the given problem:

• A(0)=$2,300

,

• r=3%=0.03

,

• t=6 years

Substitute these values into the formula:

$\begin{gathered} A(6)=2300e^{0.03\times6} \\ =\ 2753.60 \end{gathered}$

The amount in the account after six years is $2753.60 (rounded to the nearest cent).