Given:
You have $1000 to invest a year and have an account earning 4% compound continuously.
Required:
How much money will you have at the end of the year.
Explanation:
We know the formula for continuously compound interest is
[tex]P(t)=P_0e^{rt}[/tex]
Here,
[tex]\begin{gathered} P(t)=\text{ Value at time t} \\ P_0=\text{ Original principal sum} \\ r=\text{ annual interest rate} \\ t=\text{ Length of time the interest is applied } \end{gathered}[/tex]
We have initial amount $1000, annual interest rate 4% and length of time 1 year
.
Now,
[tex]\begin{gathered} P(t)=1000\times e^{0.04\times1} \\ P(t)=1040.81 \end{gathered}[/tex]
Answer:
So, $1040.81 money will have at the end of the year.
