Question

An initial amount of $3500 is invested in an account at an interest rate of 6% per year, compounded continuously. Assuming that no withdrawals aremade, find the amount in the account after two years.Do not round any intermediate computations, and round your answer to the nearest cent.

Answer 1

For this problem we use the continuously compounded interest formula:

`M=M_0e^(rt)`

where M_0 is the initial amount, r is the interest rate per year and t is the number of years.

Substituting M_0=$3500, r=0.06, and t=2 we get:

`\begin{gathered} M=3500e^(0.06\cdot2)=3500e^(0.12) \\ M=3946.24 \end{gathered}`